I'm no expert, but to me that horse looks like she could easily carry him. Maybe not every day, but you said he doesn't ride everday.
My Dad was 170 lbs. And rode my little 1/2 arab, 1/2 qh, who was only 14.2 hh. She sprang around like he weighed no more than a feather.
Depends on the horse. They can carry a lot of wt. I second asking the vet, just to be safe, but I don't think this is a problem.
If you just really arn't comfy with him riding that girl, then try for a morgan. They are incredibly strong, stout horses for their size. I have seen 300 lb. Man riding a 15.2hh morgan gelding. No problem! (Although that one did make my back hurt! LOL!)
Ask the horse. Is your back sore? How does your neck feel, how about your legs? Run your hand over and around, do a little deep rubing and see what response you get. Ear pinning? Tail swishing? Not good. Head down, deep sigh, going to sleep, very good!