Although probably capable of it and almost certainly historically used to carry that kind of weight, I wouldn't let anyone over 14 stone ride my Welsh Cob.
depends on breed - a highland or stocky welsh D would probably cope provided the rider was supple and balanced and not a sack of lard wobbling around..
hope this gives you some ideas! I dont know if some peope would disagree with me on some of the above, but they would be about what id look for. although something clydsedale/shire esk would mightly be my ideal for 17st!
no way would I expect the average built welsh D to carry 17 stone on a regular basis. You would need a traditional heavyweight cob of around 15.2hh to be comfortable with carrying a 17 stone rider on a regular basis or something like shire x or clydesdale x or Irish Draft not x with tb unless they are built more on the ID side of things.
My horse in my siggy pics carries me fine( 10st 6) but struggled with my ex YO who is a good 16stone but a light rider.My horse is 15h possibly 15.1h.