I am thinking of making my TF2 account premium, I have a couple good weapons I want to trade. These weapons currrently are "Not Tradable". If I upgrade, will these weapons become tradable?
Actually, yes. If you picked up item drops that are currently untradable, they will become tradable once you become premium. The only exception to this are Achievement items, which are always untradable (usually only tradable through gift wrap).
I tested this out using an alt account to go premium. Weapons and a spare name tag that were previously untradable became tradable the instant I became premium (bought myself a Giftapult, only 10cents).
There is an exception though. Items that are designed to be untradable by default (Achievement items, Support granted items, Badges, etc.) will not become tradable if you upgrade to premium.
To add on too lumbricus lubricant
if you have the money to buy premium go for it. You get more backpack slots(300 compared to 50) and as noted above you can trade.You also can get rare and cosmetic items and make custom blueprints.Buying the Gifta-pult(lets you send gifted items) one of the cheapest things gets you a premium account.
Also make sure that you have steam Guard on for at lest 30 days.