The vet came out and said he's fine to by jumped and ridden, as long as its not too high. She said he would only benifit from the excersise.
OK, I'd personally consider consulting a good bodyworker, who understands better about all that.
Do you see those withers?! Bareback is just painful. I ride him in my medium tree saddle with a regular pad, and a half pad.
Yes, high withered horses can be a... challenge to ride bare!
Bareback pad?? Yeah, have no idea whether or not your saddle fits him of course(tho 'medium' gullets can mean pretty narrow, depending what sort), but considering his lack of muscle, I wouldn't personally be putting much in the way of constant pressure on him, as with ANY saddle, if you're wanting to build him up.
What would you recommend for food?
Low starch/sugar & high fibre. Constant access or little & often feeding. Long stemmed(hay) roughage is generally best. Well balanced nutrition. FeedXL.com is one great resource for working out the confusion of balancing diets & finding the right products for your horse. Some high energy but low sugar 'hard feed' options include; lucerne/alfalfa, beet pulp, soy hulls, rice bran....