Spector Performer, and Legend Classic basses have a small basswood body, play well, are cheap used, (the performer can be found cheap new sometimes), they are very light, and I think they sound good.
One thing you might want to try... a really good leather padded strap could make a lot of difference on your neck and shoulder, (like a Levy's),,, they cost a lot (45 to 60 dollars), My left shoulder is in bad shape from a bike wreck, it hurts often, I play a couple of heavy Fenders, without my Levy's strap it hurts bad in the first 30 minutes, with it,, it's just a little sore after a few hours, for me it made a lot of difference, see if you can try a good padded strap, mine is the 2 1/2 inch model,, with the padding it actually measures 3 1/4 wide, probably not too wide for you.