Just wanted to add to this thread my personal experience. Until very recently we had a haffy cross on the property that was 12 hands even and 900 lbs. (For those that know the our horses I mean Willow, who has now gone to live with forum member ShutUpJoe) Although she is certainly overweight, even in slim and trim form I bet she would top out 775-800 lbs easily. Although short, she is extremely stocky. And even at only 12 hands she could have easily carried a 250 lb individual. It has much to do with the build of the horse, and haflingers or other "draft ponies" might well be an area for you to investigate, with the shorter height to make mounting easier for your father (not to mention much less distance to fall, should the worst happen) but still be well stocky enough to carry his weight.
Another area to potentially investigate is mules. Pound for pound they are substantially stronger than most horse breeds, even smaller mules can very readily carry grown men with no issue.