In my experience it's "how much weight WILL they carry"!
In the case of ours it's about 8.5 stone - over that and she'll have you off! I was told this when we bought her but she's such a good girl usually that I thought that I'd use her for transport for the quarter mile or so to the field. Not a chance, she dropped her shoulder and off I went, hadn't even got out of the turnout area!
She will quite happily pull a trap with over 25 stone in it though.