19 Stone is quite heavy but you should still be okay. Where I trained one of the instructors was a small female so she used to be put with the big students that would have otherwise been too heavy with the average instructor. You probably won't be able to train in a little C150/2 but the slightly larger 4 seaters should be okay for you.
If you find you absolotely love flying it may also incentivise you to try to lose a few stone as well!
For commercial flying you will need a Class 1 medical and I think (I may be wrong) that they work out your BMI from weight and height. They also test blood colesterol. It's been a while since I did my medical exam so I forget but you should check the medical requirements first if you only want to fly commercially. For private flying the medical requirements are a bit more slack.
Hope all that helps.