You will be able to find a board that suits (there is a
Bic 'super magnum' for example that will float you no problems).
However, you will need to physically be able to your feet pretty fast from a prone (flat on the floor) position within a pretty short time (pop up). Even if this is by front foot forward and push up then back foot (google 'aussie sprinter' pop up)
Also, for the sake of safety, before you venture out too far into the waves, you need to be able to swim at least 300m and preferably 500m at a
bare minimum (and aiming at 800-1000m), just in case you lose your board. However, probably the first few months you will spend in the shallows/in the white water, as do all beginners, so you dont need to have that skill before you start - but you need that skill before you go out further.
Otherwise, there is nothing inherently different to surfing that means you can't do it at 18 stone. Its not an easy sport to learn but suitable equipment is available; after that its up to your physical ability as it is for everyone else.