You do not lose the weapon level. You just do not get the weapon until you reach the player prestige for that weapon.
what is the benefit out of prestiging a weapon?????..... an emblem or clan tag on a gun for me thats a pointless addition in this game... you should be able to do that anyway..
It's good for extra XP, since you get XP every time you unlock an attachment. And some probably want the player cards.
Your player prestige is different from the Gun prestige. When you prestige your player you have several options. Pick one of 3 - reset your stats, cash in tokens, or add custom slot. You can also unlock a weapon, perk to keep. Weapons Prestiages allow you to add Clan Tag and then Emblem