We had the opposite problem this year. Our exchange student from Finland was 5’2″ and 100 pounds. None of our stuff fit her, except for a few of my 13-year-old daughter’s items we still had from a few years ago. So we borrowed BPing clothes from friends (in small-town Alaska, a very high fraction of families are outdoorsy). And a tent, sleeping bag or pad that is “too large” still works.
Anyway, thrift stores.
There are more XXXL garments in thrift stores than at REI. And for a lot less money.
60 years ago, everyone just backpacked in Levi’s jeans and the vast majority of them survived. So “cotton kills” is somewhat hyperbole.
But if you want to avoid cotton (and there are good reasons for that), lycra, polyester, nylon and wool clothes are all made for non-backpacking markets and those can be had for not much money when used. Nylon track pants / jacket. Wool, polyester or blended dress slacks. Looks a little odd on the trail, but they function fine. Wool sweaters aren’t as UL as a down puffy, but they might be $5-$10 and work fine.
Hats, ponchos, and trail umbrellas are really one size fits most, so maybe you or a friend have some those around.
For a sleeping bag, yeah, most BPing bags aren’t going to have enough girth (or length). So take a BPing sleeping bag and use it as a quilt. Get a 72-inch pad underneath and drape the sleeping bag over. Extend the 72-inch pad with one’s empty pack under his feet or a pillow under his head. And bring a warm beanie and a Buff/scarf if the night is cold (a good idea anytime for anyone).
For shelter, give him a 2-person tent for himself. Or a 3-person tent with one other person, etc.
A hip belt is going to be hard to do, but a 2-inch Fastex buckle set and 20 inches of 2-inch flat webbing would let you extend an existing hip belt like the seat-belt extensions on airplanes. Or go without the hip belt. I don’t like to use one unless my pack is over 30 pounds. And I have hips. At 300 pounds he might not have hips to rest a hip belt on. Keep the weight down, more through UL philosophy (don’t pack your fears, eliminate duplicate gear, embrace the funk, etc) than through more UL gear, and you won’t need a hip belt.
Inside an active big guy is a strong guy (I learned after seeing a very large friend pack out an elk hindquarter I couldn’t even lift). Still, err on the side of less miles and fewer climbs until you’ve seen him do easier stuff with no problem.