"I have a pretty big mass, (I'm overweight) what do I attract?"
Everything! But big your mass may be to you, it's tiny relatively speaking. Gravity is a weak force, remember - things have got to be pretty big for their gravity to be noticeable.
"Mount Everest is pretty massive, what does it attract?"
Everything, as above.
"The Earth is fairly large and yet the moon is actually receding from it?"
Both correct. The moon's velocity is just sufficient to cause it to be receding from the Earth at about a couple of inches a year but, eventually, it will stabalise.
"The big bang is quiet an event"
I think you mean 'quite an event'. At the time of the big bang, there was no gravity at all. In fact, there was nothing of anything at all!
"Shouldn't it all be coalescing? Not expanding?"
There was a theory for a while that there might not be enough matter in the universe for it to expand to infinity and that, at some time, it may began to fall back in on itself in a "big crunch". There was even a theory that this might already have happened more than once! However, this theory is now not widely believed and it is now thought that the universe will continue to expand until there is nothing left and the last star will simply burn itself out.