My brother plays bass and the head is so heavy you have to support the neck or it drops. I'm not sure if this is normal, but is there a way to counter balance the body of it to help keep it balanced better?
Depends on the bass - some Thunderbird owners move the top strap button to where the neck bolts on to balance it better.
I had a Tbird, still miss the sound but not the neck dive. Really not comfortable for a 2 hour set.

Get a really thick strap to increase the friction at your shoulder and suede is good as it grips better. Wear the bass higher than normal or low, there's something about the normal height that seems to create problems.

The only reason I sold mine was this issue, there is no real long term cure. You have to live with it in the end, or not.
Some basses are like that. One way to stop the neck dive is to move the rear strap button about three inches lower than it presently is, then add a second rear strap button about four or five inches above that. Cut a second hole in your strap for the new second rear strap button. By securing your strap with three strap buttons so arranged, it goes a long way to stop the neck dive. It works very well for bassist Bunny Brunel.
"Maybe this world is another planet's hell?" - Aldous Huxley
Other options would be to swap the tuners with light weight replacements. You can also try to counter balance with small weights.
My friend has a Thunderbird, and has very few problems with the neck dive because he uses a very wide suede strap, like others have mentioned.
Don't know if you've got this sorted yet but I've almost cured the problem on both my T-bird and Warlock using BBs from the local airgun shop.
Open up the back plate, cover the electrics with a few layers of cling film, fill the cavity with BBs, replace back plate and cut off excess cling film.
OK, the T-bird is now over 500g heavier but at least I can let go of it without fear of it dropping....