Weapon upgrade system in Final Fantasy XIII

I'm well into disc 2 and I'm still a little lost with the weapon upgrade system.

I don't know how to compare the weapons when they are different levels, and I'm also a little confused when choosing components to rise their level. Could anyone help?

Two of the best weapon components you can buy (cheap and effective) are Sturdy Bone (80 Gil) and Superconductor (840 Gil).

All you have to do is continuously pour Sturdy Bones into your weapon, until it tells you that you have a 3x bonus (should take at least a couple dozen). When this happens, pour as many Superconductors as you can afford into that weapon. This is effectively the best strategy for turning Gil into weapon levels, and it worked great for me.

The general stradegy is to add organic components (indicated by the claw icon) to the weapon to add to its bonus multiplier. Once the multiplier reaches its maximum (x3), add a bunch of mechanical components (indicated by the bolt icon) at once. This will empty the bonus multiplier, but boost the experience of your weapon significantly. Thus, if you have a few particle accelerators lying around, you can use those in place of superconductors.

If you're lucky, the weapon's level will be replaced with a star. When this happens, you'll need a special item to upgrade it to its next form. Most of these items can be purchased at The Mother Lode. This upgrade will allow you to continue levelling the weapon. Note that each weapon can be upgraded twice - once around level 26 (different weapons take different catalysts at this stage), and again at around level 61 (this always takes a Trapezohedron).

All in all, you won't need anything more than a level 61 (starred) weapon to complete the story missions of the game, but if you want to get all the final weapons, you'll need six Trapezohedrons, which cost around 2,000,000 Gil each. See other guides for best places to farm Gil and rare components.

AFAIK, comparing final stats of weapons isnt possible ingame, although after upgrading a weapon once or twice, it is not difficult to see what the stats will be close to (i.e. strong magic, medium str etc)

Now being gamers and perfectionists (and lazy) this isnt the best thing. So i recommend using this guide to help you make your decisions. It has the base stats as well as the final stats of all the weapons. This means you dont have to waste your time upgrading weapons only to find out the final product isnt quite as strong as another.

It is generally agreed upon that the best method to upgrade is to use organic compounds first (I think its organic, im referring to the claws and teeth and these materials) to raise the exp boost to 3x, then use non-organic to take advantage of the 3x.

Note that when a weapon maxes out, any extra exp will be wasted. Therefore to optimize you will want to know the max exp of a weapon, so you can use as little organic materials as possible, then pump non organic materials in one go without going over.

There is a more detailed explanation of the whole system here

Hope this helps