You can tape it all up before you go to the post office. Make sure you package it very securely, as stuff going to military people overseas is not exactly handled gently.
At the post office, they have customs forms you will need to fill out. If you tell someone there you are sending to military address overseas, they will show you which form to use. I send care packages often, so I tend to grab a small stack to use for future packages. Then I can fill them out at home rather than standing at a counter (just my personal preference).
In my experience, care packages have always been weighed. But perhaps in your situation there is a special exception that you're referring to. If you mean flat rate envelopes, such as Express or Priority Mail, those rates don't usually apply to military addresses overseas.
I usually make my own label, with 1/2 sheet of plain white office paper & a Sharpie marker. Then I use clear packing tape to secure it to the box & completely cover the label (making it smudgeproof). They will also attach your customs form to the box, but I like having a more clearly visible address on there to make it easier for those trying to help the package along its way.
I've never been asked for ID, unless paying with debit card. :)
As it's getting warmer, be sure not to send stuff that can melt! Chocolate, chapstick, etc. will all be liquid by the time it reaches Kuwait.
Also, it's a good idea to double bag everything in zip-locs. Even if you think it can't leak, it just may. I can't imagine many things more disappointing than getting a package, & opening it to find it's ruined & unusable. And send food stuff separately from hygiene stuff. Even if everything is all sealed up, the harsh conditions of shipping have been known to make cookies & candy taste of shampoo & soap. Blech!
You're a great friend for letting him know how much you care! :)