Do weapons increase any "useful" stats as they level up in MP; like SP?

Me and a friend were playing MP and where I've mostly been playing SP he has mostly been playing MP. This obviously led to a drastic differences in our guns. Most of mine were at III or less and most of his commons were at X. Curious we compared the stats and the only things that got better on the guns comparing a I weapon to an X weapon was weight, accuracy, and i think we had one where the ROF went up slightly.

I was shocked seeing how in single-player the weapons drastically get better as you level them up. I'm honestly just hoping my friend was screwing with me and the DMG, Clip Size, or something else that actually helps the gun goes up. I mainly play classes like the Aerial Havoc Trooper or Krogan Merc so weight to help recharge rate is useless to me. Also, a lot of these guns just seem to suck even on bronze so if they don't improve with levels then I guess I'm stuck using he Equalizer and Lanat for the rest of my MP career.

If the above is true for most, maybe all weapons, what's the significant difference between an I weapon and an X weapon? Does anybody have any numbers going against this?