Blatently obvious. If a fat person tries to sneak round a corner they will be seen, as their belly will protrude first and give them away. Hence if something can be seen a mile off, or is really obvious, it can be 'seen coming like a fat man round the corner'
Really really really sweaty. Imagine a chubby fellow dining out at his local pastry shop - he stands, salivating, over the counter wondering which fatty treat to shove down his gullet, and then indecision strikes and he sweats over what to order. That's how sweaty you are if you're sweating like a fat man in a cake shop.
Incidently, if you are a fat person and want a way to avoid such problems as choosing which cake, my advice is to simply buy everything. Problem solved
Kirsty: 'How was your squash game?'
Jim: 'Great, but now I'm sweating like a fat man in a cake shop.'