Does my lower weapon proficiency go up quicker late game?

When I kill an enemy I get EXP of sort to my Weapon Proficiency. I often don't use rocket launchers as much as I do SMGs or Combat Rifles and I have not used Revolvers at all despite having a really powerful Purple named revolver i got from a Boss (can't remember which one).

If i wait to late game when enemies are higher level does lower weapon proficiency go up quicker to catch up?

Yes, your weapon proficiency will increase faster the more difficult the enemy you fight is.

A user in this Reddit post states:

Usage. Some enemies give more proficiency points than others though (and weak ones don't give that much so killing thousands of lvl01 guys ain't very productive). Go to the Eridian Promontory kill some guardians and watch your proficiency skyrocket

It is also verified on this Arqade post:

From what I know the proficiency you gain is dependent on the XP you receive from the kill. If you damage an enemy with a weapon and the enemy dies you get proficiency even if something else kills it eventually. You might get more though if your weapon does the kill. So, no fixed number of kills for a level up.

Waiting until late game and then grinding out high-level enemies is a great way to level your weapon proficiency