It's an awfully awkward situation, but I can see why you're concerned.
I'd be wary, OP, I've got to be honest. We have a friend who is a similar size, from the sounds of things, and, like others, we have had damage (expensive damage!) on a couple of occasions to our car from giving lifts to them. That's aside from the fact that it really does noticeably affect the handling and steering. DH refused to drive on a motorway with them after the first lift; my sister said the same after she gave one, and she was driving much newer and much bigger car than we have.
They got their own car a while ago. Friend can't drive; partner works away a lot so it gets used max 1 x per week. They've been replacing seats/shocks/wheel bearings etc on the front passenger side on a six monthly basis since they got it. Its flagged a fail on all three MOT's so far for some major component in that area. Partner has admitted he's been told it's the excess weight that's the cause by their mechanic.
Cars are tough, yes, but they're designed for average weights. Bear in mind that a very tall 6'3" man is considered obese at around 17 stone, and that 15 stone is more normal 'heavy bloke' weight, there's no reasonable way that the car (or any car) was built with these sorts of weight in mind for a single passenger. It's a mass that's pretty much twice what would have been envisaged by the designers. Generally speaking, mechanical systems don't generally cope well being run 40 - 50% above their design tolerance, and it is a risk that things will fail, especially on an older car, where components may be coming to end of life anyway.
They haven't asked, OP, and I wouldn't offer.