My Canadian mare is 15.2 hands, and could easily carry a 250+ pound person, I'm only just barely hitting 5 feet tall and my weight matches my height :P you can guess by the pic xD So I guess me being so short makes her look taller xD but she's quite round! I think any tall person could easily ride a horse her size/shape.
I just love them! Morgans seem to carry the same gene as Canadians in being great weight carriers. Most are fairly short coupled which makes them better at carrying weight. I could see a typical 15-16 hand morgan carrying a tall adult person. Many big men ride normal Morgans (the typical style, not the itty bitty new style morgans). I ride a new style Morgan at work o.o It feels like riding a caterpillar- I feel too heavy for her, but she carries me and bigger riders than me quite comfortably. So even those skinny little new style ones are still decent weight carriers for their size. I wouldn't worry so much about it