I cartop a Wilderness Systems Ride 115 on a Toyota Corolla... There's no reason you can't do it on a Fit (not sure if it comes with racks standard or not) with a kit like this:
http://www.seattlesportsco.com/car-top/block-kits/riversider-universal-kayak-carrier-kit.html
Any shop that sells kayaks (EMS, Dicks, etc) will have these kits - and for way less than is on that site. You can invest more (roof racks, J-cradles, etc) but you don't need to...
As far as boats go, there are TONS of fishing kayaks now that would easily support you and your bring-along gear. The Ride 115 that I have, for example, is dead stable for me and I'm just a little south of your weight. I even take our ten year-old riding on the bow with me from time to time and never think twice about bringing our four year-old guy in the same boat. I think the rated capacity is 450lbs. So, plenty.
I also just paddled a stormy CT river in a regular, 12ft cruising kayak rated for less than my weight. Once you learn to keep your weight centered - which is admittedly harder when raring into hooksets - you can paddle and be 'safe' in nearly any boat within reason.
The market has grown leaps and bounds since I bought my boat, so you'll have to shop... But you should have no problem finding a kayak that will easily get you on the water - even allowing you to stand if you're somewhat graceful with your balance.
A couple notes:
None of the big, modern, high-stability kayaks are water-burners. They are slow and tubby for their length. So, think about the kind of water you fish and set your expectations accordingly.
Also, PADDLE AS MUCH AS YOU CAN BEFORE YOU BUY. There is nothing that will tell you more about what you like/don't like, what suits your comfort in terms of stability, etc more than actually putting your butt in the seat of a boat and paddling. There are demo days for kayak stores all over, so look for those. Or, find a bunch of local kayak anglers and ask if you can go with them. Most will have a spare boat you can use and will be happy to let you take a couple seconds in the seat of theirs.
IF you must buy without paddling, I'd avoid the bargain brands (Pelican, anything from StuffMart, etc) and go with a recognized brand/model... It may not be perfect, and you might be missing a bargain. But, you'll not have MAJOR regrets, either.