Do the “weak and ill suited for battle” weapons have any hidden stats or bonuses

It doesn't change the story in any way but it does change the amount of enemies and the location of them on missions while making them significantly stronger and with different items + skills. The only way to get different storyline is to change your gender during another playthrough and have the characters marry different people. Please note that I haven't finished my Lunatic playthough but haven't seen any differences so far. Also, this is expected as the script writers had TONS of stuff to write already (most of which you will never be able to read), so this is most likely just a gameplay difficulty.

Spoiler: Lucina will have different dialogue with you if you are married to her throughout the game. You can also marry Chrom which will produce a slightly different story.

The challenge factor from these types of turn-based strategy games tend to come from the following:

• Your resources are generally fixed - you can't grind for more or delay an engagement while you (over-)prepare
• Mistakes made early tend to compound to the point that if you make errors early, you're likely to continue to feel the effects late into the encounter/game
• The game mechanics and systems involved tend to be complicated and deep

In every encounter, there's generally a tipping point - some point at which the encounter has been won by one side, but there's just the messy matter of meeting the requirements for success.

The way I tend to tackle this type of challenge is by iterating and careful analysis. For instance, let's say you're playing XCOM:EU.

You get halfway through a battle and two of your soldiers are dead. The enemies are quickly overwhelming the rest of your squad. At this point, you're probably past the tipping point - the enemies already killed two of your soldiers, and you started out outnumbered. Now is a good time to take a step back.

At what point did I start to lose? Well, probably when one of my guys died.

Why did he die? Well, he was in a bad spot and got ambushed. There were a couple of lousy dice rolls that contributed.

Now I've reached a point at which I had control and made a decision. I can't have predicted the ambush with 100% certainty, and I can't influence the random number generator, but I probably could have anticipated that things were going poorly, and put him into some better cover or had him fall back. Having identified a choice that I had and didn't do a good job of making, I can iterate on my strategy and try again.

The compounding factors are the same as our challenge items from before. For instance, changing this decision might not be enough to effect the outcome. I may have made a tactical error earlier in the fight, or I may have brought the wrong people into combat, or I might have made a mistake in outfitting them, or even earlier when leveling them up.

Tracing these sorts of issues back to their root can be challenging, but it's the only way to improve. This is one reason that, when faced with a game that I know is going to be challenging, I'll start on a lower difficulty level or in a mode that allows me to restore my state from earlier. That way, I have the option of rolling back more of my decisions. When I can play flawlessly, losing no resources and inflicting maximum harm, I turn the difficulty up a notch and see where the leaks in my strategy are when the computer is playing smarter.

Part of this is a learning process - learning how to best utilize your limited resources requires an understanding of the game mechanics that doesn't come easily. Part of this as well is patience - most of the time, these games aren't rushing you, so you can take your time and make sure you're making the most of your environment.