I second the others who suggest a shorter, stockier type horse. What you will want to look for is a thick horse with a wide chest, thick leg bones, and big feet like the pictures that have been posted here. A short back and a big barrel are also good indicators of weight carrying ability. I have a Mustang that is 14.3 and due to his thickness, I wouldn't hesitate to put someone heavier than you on him.
I am the same height as you, littlehoof, and I don't think I would go for anything terribly tall. For me, anything much over 15.2 gets difficult for me to easily mount without a block or a hill. A cob of some sort or a draft cross would work wonderfully, I'm sure. I am not sure about the temperaments of cob horses (I have no experience with that breed), but in general, draft crosses seem to be more mellow.