Two-Weapon Fighting is best for DPR

TL;DR: The Heavy weapon causes the Halfling to miss too often, losing a lot of DPR and the damage from the second attack of Two-Weapon Fighting is greater than the damage gained from the higher damage die. Eldritch Blast is a very poor option before level 5 if you don't have the Agonizing Blast invocation.

Heavy vs Versatile

First let's compare Heavy weapons with Versatile weapons wielded in 2 hands. A Heavy weapon's 1d12, on average, deals 1 more damage on a normal hit and 2 more damage on a critical hit when compared to a Versatile weapon's 1d10. So, if we multiply these damages by hit chance and crit chance, we can arrive at how much damage a Heavy weapon deals over a Versatile weapon (for a Medium creature).

Regular Hit Formula: \$HitChance=\frac{(20-(Target AC - Attack Bonus))}{20}\$

\begin{array}{c|c} \text{Target AC}&\text{Damage Difference} \\ \hline 10&0.85 \\ 11&0.8 \\ 12&0.75 \\ 13&0.7 \\ 14&0.65 \\ 15&0.6 \\ 16&0.55 \\ 17&0.5 \\ 18&0.45 \\ 19&0.4 \\ 20&0.35 \\ 21&0.3 \\ 22&0.25 \\ 23&0.2 \\ 24&0.15 \\ 25+&0.1 \\ \end{array}

Formula: \$Regular Damage+Critical Damage=1*HitChance+2*0.05 \$

However, Halfling are small, so they have disadvantage on checks with Heavy weapons. This means there is a 95% chance that a critical hit is not one and a chance that a hit becomes a miss. This means the entire damage of the attack (or extra die) is lost, and that damage loss is shown in the following chart:

\begin{array}{c|c} \text{Target AC}&\text{Loss from Disadv} \\ \hline 10&1.83 \\ 11&2.09 \\ 12&2.30 \\ 13&2.47 \\ 14&2.59 \\ 15&2.66 \\ 16&2.68 \\ 17&2.66 \\ 18&2.59 \\ 19&2.47 \\ 20&2.30 \\ 21&2.09 \\ 22&1.83 \\ 23&1.52 \\ 24&1.16 \\ 25+&0.76 \\ \end{array}

Formula: \$Regular Loss+Critical Loss=9.5*HitChance*(1-HitChance)+6.5*0.05*0.95 \$

Since at every relevant AC, the loss is greater than the damage gained from the higher damage die, all other things equal the Versatile weapon is better than the Heavy weapon for the Halfling.

Versatile vs Two-Weapon Fighting

Now that we know Versatile is better than Heavy at all Armor Classes, let's compare Versatile and Two-Weapon Fighting. First consider only the first attack. A Versatile weapon's 1d10, on average, will deal 2 more damage on a normal hit and 4 more damage on a critical hit when compared to a Light weapon's 1d6. We follow the same procedure as with Heavy vs Versatile and see the damage based on target Armor Class.

\begin{array}{c|c} \text{Target AC}&\text{Damage Difference} \\ \hline 10&1.7 \\ 11&1.6 \\ 12&1.5 \\ 13&1.4 \\ 14&1.3 \\ 15&1.2 \\ 16&1.1 \\ 17&1.0 \\ 18&0.9 \\ 19&0.8 \\ 20&0.7 \\ 21&0.6 \\ 22&0.5 \\ 23&0.4 \\ 24&0.3 \\ 25+&0.2 \\ \end{array}

Formula: \$Regular Damage+Critical Damage=2*HitChance+4*0.05 \$

However, When using a Light weapon, the warlock can use Two-Weapon Fighting to get another attack. This other attack doesn't add the ability modifier, but still increases damage by an average of 3.5 on a hit and 7 on a crit. Here is the damage from second attack modified by hit and crit chance:

\begin{array}{c|c} \text{Target AC}&\text{Second Attack} \\ \hline 10&2.98 \\ 11&2.8 \\ 12&2.63 \\ 13&2.45 \\ 14&2.28 \\ 15&2.15 \\ 16&1.93 \\ 17&1.75 \\ 18&1.58 \\ 19&1.4 \\ 20&1.23 \\ 21&1.05 \\ 22&0.88 \\ 23&0.7 \\ 24&0.53 \\ 25+&0.35 \\ \end{array}

Formula: \$Damage=3.5*HitChance+7*0.05 \$

Since, at every relevant AC, the damage from the second attack is greater than the damage gained from the higher damage die, all other things equal Two-Weapon Fighting is better than the Versatile weapon.

Eldritch Blast?

Eldritch Blast is even worse than a Versatile weapon at level 4. Since the warlock does not add Charisma modifier to damage from eldritch blast, the spell loses 3 damage on a regular and critical hit when compared to the Versatile weapon. Here is the Damage Difference between 1 attack of a Versatile weapon and an eldritch blast beam:

\begin{array}{c|c} \text{Target AC}&\text{Damage Difference} \\ \hline 10&2.4 \\ 11&2.25 \\ 12&2.1 \\ 13&1.95 \\ 14&1.8 \\ 15&1.65 \\ 16&1.5 \\ 17&1.35 \\ 18&1.2 \\ 19&1.05 \\ 20&0.9 \\ 21&0.75 \\ 22&0.6 \\ 23&0.45 \\ 24&0.3 \\ 25+&0.15 \\ \end{array}

Formula: \$Regular Damage+Critical Damage=3*HitChance+0*0.05 \$

Since the Versatile weapon is already established as worse for DPR than Two-Weapon Fighting, eldritch blast also falls short (although it does beat out Heavy weapons at low Armor Classes).

Summary Table

I've been doing comparisons throughout this answer to show how flexible math can be for figuring out differences between a few different options saving some time on doing the entire damage calculation. But here is the entire damage calculation for the sake of completeness:

\begin{array}{c|c|c|c} \text{Target AC}&\text{Heavy}&\text{Versatile}&\text{Two-Weapon}&\text{Eldritch Blast} \\ \hline \text{10}&6.41&7.08&8.35&4.68 \\ \text{11}&5.67&6.65&7.85&4.4 \\ \text{12}&4.98&6.23&7.35&4.13 \\ \text{13}&4.34&5.8&6.85&3.85 \\ \text{14}&3.75&5.38&6.35&3.58 \\ \text{15}&3.20&4.95&5.85&3.3 \\ \text{16}&2.7&4.53&5.35&3.03 \\ \text{17}&2.25&4.1&4.85&2.75 \\ \text{18}&1.85&3.68&4.35&2.48 \\ \text{19}&1.49&3.25&3.85&2.2 \\ \text{20}&1.18&2.83&3.35&1.93 \\ \text{21}&0.92&2.4&2.85&1.65 \\ \text{22}&0.71&1.98&2.35&1.38 \\ \text{23}&0.54&1.55&1.85&1.1 \\ \text{24}&0.42&1.13&1.35&0.83 \\ \text{25+}&0.35&0.7&0.85&0.55 \\ \end{array}

Formula: \$Regular Damage+Critical Damage+Second Hit+Second Damage=\frac{Damage Die+1+2*Modifier}{2}*HitChance+2*\frac{DamageDie+1}{2}*0.05+\frac{Damage Die+1}{2}*HitChance+2*\frac{DamageDie+1}{2} \$

note: eldritch blast consists of only a second attack in this formula and the Heavy column has Disadvantage factored in (square HitChance)

Level 5

Level 5 changes things a lot. Eldritch blast gets a second beam, your proficiency bonus increases, and you get access to Thirsting Blade and Eldritch Smite as Eldritch Invocation options if you want to choose them. Since you said you choose Invocations for roleplay purposes, I'm going to assume you did not choose a combat Invocation for this table (if you want to know how to maximize the functionality of one of these invocations, I suggest you ask a new question). Below find the adjusted table for level 5:

\begin{array}{c|c|c|c} \text{Target AC}&\text{Heavy}&\text{Versatile}&\text{Two-Weapon}&\text{Eldritch Blast} \\ \hline \text{10}&7.19&7.5&8.85&9.9 \\ \text{11}&6.41&7.08&8.35&9.35 \\ \text{12}&5.67&6.65&7.85&8.8 \\ \text{13}&4.98&6.23&7.35&8.25 \\ \text{14}&4.34&5.8&6.85&7.7 \\ \text{15}&3.75&5.38&6.35&7.15 \\ \text{16}&3.20&4.95&5.85&6.6 \\ \text{17}&2.7&4.53&5.35&6.05 \\ \text{18}&2.25&4.1&4.855&5.5 \\ \text{19}&1.85&3.68&4.35&4.95 \\ \text{20}&1.49&3.25&3.85&4.4 \\ \text{21}&1.18&2.83&3.35&3.85 \\ \text{22}&0.92&2.4&2.85&3.3 \\ \text{23}&0.71&1.98&2.35&2.75 \\ \text{24}&0.54&1.55&1.85&2.2 \\ \text{25}&0.42&1.13&1.35&1.65 \\ \text{26+}&0.35&0.7&0.85&1.1 \\ \end{array}

Note: the formulae are the same as for the level 4 table, but the eldritch blast column is doubled since there are now two beams

As you can see, without a combat invocation, eldritch blast surpasses the weapon options at level 5 even without Agonizing Blast.

With only a pact weapon, you can only make two attacks

Thirsting Blade says:

You can attack with your pact weapon twice, instead of once, whenever you take the Attack action on your turn.

And Arcane Armament says:

Starting at 5th level, you can attack twice, rather than once, whenever you take the Attack action on your turn, but one of the attacks must be made with a magic weapon, the magic of which you use to propel the attack.

Note that Thirsting Blade does not say that you get to attack "one extra time" with your pact weapon. It says you get to attack twice when you take the Attack action with that weapon. Thus, if you are using only that weapon to make your attacks, you will only be able to attack with it twice per Attack action. Arcane Armament just adds a different way to achieve two attacks - but neither ability will give you a third attack in this situation.

What if you make one attack with a weapon that is not your pact weapon?

Take this example: you made one attack with a non-pact weapon, dropped it then made the second attack of arcane armament with the pact weapon.¹

In this case, it actually creates a slightly ambiguous situation if you read it strictly by RAW.

By RAW, Thirsting Blade allows you to attack twice with your pact weapon specifically, and Arcane Armament allows you to attack twice in general; both effects trigger off of the above situation. If an ability is triggered, you should be able to benefit from its effects unless they are prevented by something else. The only way for both of those abilities' effect descriptions to be accurate would technically be to allow another attack with the pact weapon. And there is seemingly no rule preventing this from happening.

However, this is almost certainly not the intent at all. The fact that Thirsting Blade explicitly was added as an exception to Extra Attack (which is almost identical to Arcane Armament) tells us that the kind of interaction is not intended. Note that the artificer is in UA, and not all UA is balanced or tweaked for multiclassing. This is likely just a case of a loophole they haven't gotten around to addressing or noticing yet, but I'd expect it to be fixed upon official release.

^{1 - Two-weapon fighting would not work here, however, since the bonus-action attack is taken after the Attack action and not as part of it.}