At only 6 weeks old, and being a stray, I would think 1.8 lbs isn't too terribly small. He is still just a baby.
Thinking back, we had a waterbed when we first got our cats. Even with those little kitten needle-claws they never poked a hole in it, and we played on it (with comforters on it) every night, and they always slept with us. I don't think it was a special kind of mattress - just a water bag. I think they make them much tougher now than they used to.
And we always made sure that we made the bed when we weren't in it so there was always comforters and pillows covering most all of it.
As for where to put his bed, I would just watch and see where he likes to sleep and put the bed in that area. Being that young, and a stray to boot, he may want to be more hidden when he's vulnerable sleeping.
Can't wait to see pics of little Parker. Most of us have to live with kittens vicariously through others here.