could this work?
No. All weapons with the "heavy" property have the two-handed property as well. Here's exactly what each property does (PHB 147):
Heavy. Small creatures have disadvantage on attack rolls with heavy weapons. A heavy weapon's size and bulk make it too large for a Small creature to use effectively.
Two-Handed. This weapon requires two hands when you attack with it.
The heavy property itself isn't a problem here, but the two-handed is. Since all heavy weapons are also two-handed, you must use two hands to wield them. The enlarge spell doesn't give you the ability to wield a two-handed weapon in one hand, even if that weapon wasn't enlarged with you. Your DM might allow it, but it's certainly not part of the Rules As Written.
So what can you dual wield, then? Here's the rules on two-weapon fighting (PHB 195):
When you take the Attack action and attack with a light melee weapon that you're holding in one hand, you can use a bonus action to attack with a different light melee weapon that you're holding in one hand. You don't add your ability modifier to the damage of the bonus attack, unless that modifier is negative.
Based on this, you can only dual wield light melee weapons. You don't even need the two-weapon fighting style, since all the fighting style does is allow you to add your ability modifier to the bonus action attack. There is a way to get around the "light" limitation, namely the Dual Wielder feat (PHB 165, emphasis mine):
You master fighting with two weapons, gaining the following benefits:
- You gain a +1 bonus to AC while you are wielding a separate melee weapon in each hand
- You can use two-weapon fighting even when the one-handed melee weapons aren't light
- You can draw or stow two one-handed weapons when you would normally only be able to draw or stow only one.
This feat allows you (among other things) to use any one-handed melee weapons for two-weapon fighting.
In conclusion, you're not going to be two-weapon fighting using greatswords, even if you're enlarged. The closest you're going to get would be two longswords with the Dual Wielder feat
Side note: If you want to do two-weapon fighting purely from an optimisation perspective, you may want to reconsider. It is generally accepted as one of the weaker playstyles, as it uses your bonus action to be effective (needed to cast smite spells on a paladin, for example), and still can't quite compete with great weapon fighting, especially if you factor in the Great Weapon Master feat. It doesn't fall completely behind other playstyles, so if you want to do it because of a character concept, go ahead. But if it's exclusively for optimisation, it might be better to just use a single greatsword.
No
Spells do only what they say they do - Enlarge increases the size by 1 category and increases the size of the weapon (doing more damage) but does not increase the reach of the weapon.
Remember that a creature enlarged from medium to large effectively increases reach by 5 feet (more or less) anyway since it now occupies 10 feet of space rather than 5. Small to medium enlargements do not get this.
Best Answer
The gargantuan animated object continues to be animated.
In this tweet Crawford claims that:
So whether a gargantuan animated object continues to be animated, hinges on what a valid target is for the animate objects spell. The relevant limitation is this:
However, the animate objects spell also says that:
Moreover, as Slagmoth explains in this answer:
Therefore, enlarging a huge animated object doesn't make it an invalid target of the animate objects spell, because you enlarged a creature, not an object.
In other words, to make the target of the animate objects spell invalid, you must enlarge the object. However, that's impossible to do for the duration of the animate objects spell because there is no object for you to enlarge.