I think this is probably why you're finding it so tricky. There's a big difference between twelve and fifteen stone in terms of the type of horses you can be looking at.
For example, a decent quality Welsh Cob would easily carry twelve stone. However, I would not feel comfortable with one carrying fifteen stone. Welsh Cobs are fantastic; they're super versatile, relatively close to the ground, and are generally quite reasonably priced. I wouldn't necessarily recommend a pure-bred though, as they're a bit like TBs in a Cob body!
Fell ponies, Dales, Highlands, Haflingers and Fjords should all be capable of carrying twelve stone, too.
ok so heres the compromise well sort of- she is a kwpn x cob and has a small cataract in one eye ( hence 1k off the price ) apart from that she is bloody perfect and everything on my wish list !! 15.3 11 years old and well mannered , forward but safe and kind, already stolen my heart away, today i lunged her for the first time bearing in mind she was in a 30x60 school and has only hacked a few times in the past year she went beautifully, i took all the gear off her and free schooled her and she was amazing, controlled purely by voice commands and hand gestures quickly picking up exactly what i was asking her, following, turning, halting, standing still, with nothing but body language, admittedly she did get a bit distracted for a few minutes by a pony next to the school and i let her have her few minutes, but after i asked her back to me she came straight up, and continued on - really cant of asked for anything more for our first time in the school together !
she's lovely, i love her ears! For information H&H has a very comprehensive article on cataracts this week which you might find of interest. I hope you have a long and happy partnership with her.