Does anyone know an easy way to upgrade weapons. All I've been doing..

A lot of weapon upgrading is weapon specific. Take for example:

Holo-Shield: Toss some in front of the turrets (battle missions) in front of 'noid bases. Wait. Done.

Any long range weapon: Stand near the edge of the starting platform on Mylon. Snipe/shoot the two enemies for MEGA EXPERIENCE. Drown yourself in lava. Repeat.

Rift Inducer: You could use it in the sewers (Amoeboids fill the bar so fast when they keep getting sucked in. But it's easier to just use it as a primary weapon. I do, because it's a great weapon.

Guns in Annihilation Nation: Any "weapon challenge" will give you a good deal of expereince to at least get your gun to level three quickly.

Infector: Use on the regular robotic minions (Daxx, Obani, Zeldrin, Koros, etc...) they will shoot their buddies, and get massive experience for doing it.

Any "non-mega" weapon: In the first part of change mode, all starting weapons level up really fast.

Bouncer: tough luck dude, this weapon takes like, 30,000 years to level up, even when it's a regular weapon in non-challenge mode. It's worth it, though.

Plasma Coil/Shield Charger: Run through Mylon repeatedly. You get sooo much experience for the 4-eyed metal 'noids.

If desired, your could do the 1st stretch of Koros instead. As an advantage, Koros is loaded with cast (100,000 at least, even more in challenge mode (multiplier))

Or, for any weapon:

Battle field missions have a lot of valuable noids that give a lot of Exp.

Battling through Koros or Mylon with anyone.

That's all for now.

If your up to the command centre, keep on killing the guys and the guys give you maximum nano power for the gun or bomb.