I’m a fluffy gal. I’m also short and because of how I carry my weight I look heavier than I actually am. I also have some muscle under the blubber. I claim couch potato status especially after long stressful work days but as part of my lease with a private owner I carry feedbags and I walk on foot and trim trails that are uphill and downhill and more of a hike than a scenic park stroll lol. Point being I’m not a complete sack of blubber I’m just insulated for the winter. 
Barn owner knows my weight and she’s been in the horse business her entire life. She puts me on small horses/ large ponies. Especially if it’s a new one who isn’t being a sweet angel. Or one of the old barn regulars who has a tendency to buck and no one else wants to ride the adorable little turd.
When I first started riding at the barn I was worried I was too heavy and discussed it with barn owner. My first few rides I was on a larger saintly horse until she got to know my riding and evaluate it with her own eyes. (For what it’s worth I’m at the upper limit of the small horse and large pony weight limit hence me being worried about being too much). Barn owner also enforces the weight limits for her barn horses. She’s directly told riders they were above Dobbins weight limit when the riders have asked for a specific horse.
The private owner I lease with also knows my weight etc. she’s seen me in the barn horses so she also knows how I ride. I usually ride one of her small horses. A sweet adorable mare who thinks bolting is the bees knees. 
The only barn drama I’ve been in was other people and rail birds telling barn owner and private owner I’m way too fat and I’m going to hurt the pony. None of the ponies or horses I’ve ridden have shown signs of being in pain etc. That was a concern of mine after the railbirding especially with the private pony due to how much I ride her. Her owner, her vet and her farrier all told me I’m fine and pony is perfectly happy with me on her. Except when I shut down an attempted bolt.
As for my riding background- I’ve been riding since I was little. I was lucky a family friend owned horses and would frequently invite my grandfather and me to ride with him. in middle and highschool I took English lessons. Then life happened and I was out of riding until my late 20s I became a re rider. Back into lessons too- both under saddle and groundwork. I’d rate myself advanced beginner or intermediate and mediocre at best. I’m not an elegant or pretty or fancy rider. The only thing I’m somewhat decent at is quiet hands and somehow I have a fairly sticky seat. I’ve sat bucks and spooks and spins and sideways teleportations at a full gallop on the trails on dainty catty Arabians etc. (I’m not tooting my own horn. Theres many riders way better than me out there. My trainer also says I don’t suck as much as I think I do but I’ve seen videos and pictures of myself lol)