You sound like you are feeling sensitive. I don't think it has anything to do with "fat people shouldn't ride". I think it has more to do with the fact that these riding facilities are using these horses 4 to 6 hours out of the day. Many facilities have way more students then horses so they they are over booking the animals.
Lesson horses tend to end up with many issues such as arthritis, sore backs and mouths, etc. from the pounding and "abuse" they take from all of the different levels of riders that are on their backs.
Trail barns usually tack the horses up in the AM and send them out on 2 or 3 trails a day.
They are "prejudice" against heavier riders (not fat). They don't general have a rule that says "If your belly hangs over your belt line you aint riding". It's more like weight limit: 250lbs. That would exclude not only out of shape riders but some pretty sexy hot men from a ride just because they are massive. Not fat.
For what it's worth, i am definitely not "fat" by any stretch of the imagination, but i do tip the scales at 275#.
When my girl and i discussed the parameters needed for a horse for me to be both fair to the horse and it's health, as well as me and my needs, we set a few "must have" criteria-
16 hands or larger, stout build, and WIDE bodied, preferably one resembling a bus or tank.
My weight, plus my size (6'4") sort of dictates which horses i can and cannot ride, being fair to the horse.
Yes, i weigh more than many "fat" people, and there are some flat enormous folks out there too that dwarf me.
I suspect that it's the horses that the stables are concerned about.
The horses are their cash cows, and if a horse gets broken, thats less revenue possible.
I also understand the flipside of that coin, too, in that many stables have a couple larger horses for the larger people.
But, i also get the "big people"s perspective too. They want to ride, and well they should at that. But, i suspect the rub comes from not understanding that horses have limits too, and to flop a 500# man on a 14 hand horse just isnt reasonable or safe. The horse may try to toss ol' Tony Bagadonuts, or roll over to get him off, causing harm to both horse and rider, which serves nothing.
Large people are generally quite sensitive about the subject, as they are often the target of ridicule and harassment on the subject. Understandably so, i think.
If you were the target of hurtful comments and the like, how would you feel?
Now, imagine going through your entire life in that scenario, and NOW how do you feel?
So, to attempt to put some perspective onto this discussion, i would like to think it's primarily about the welfare of the horses, as well as the welfare of the people involved.
We all want to have a good ride, and bring our horse as well as ourselves back in one piece and none the worse for wear.
Or, am i on crack?