1) How overweight are we talking? Some components have sprigthly suggested weight limits, like 200lbs for Alpha and Reynolds carbon forks, and 180lbs for ti-spindled Speedplay. And 2) what have you tried?

My suggestion (not knowing your weight) would be a decent mountain bike to start with. Many sprint races even have entries for fat tire bikes (mountain bikes). When ready, you can buy "street slicks" tires for your bike too. Once you decide to move to a road bike, you'll have a spare as well as something you can take off road.

I'd suggest if you go for a road bike, you get some tires that will accept high tire pressure (at least 140lbs) Good luck!

E,
How much weight are we discussing? I'll give you my story and hope this provides you a good frame of reference.
I started at 5 foot 7 inches and 205 pounds on January 1, 2009. I purchased at Giant Defy for $1,300 with Shimano 105 components. I'm still 5'7" but now 193 as of today.
Another option to consider is Spinning classes at your local gym. I still participate 2 -3 times a week. The instructors are awesome, they kick my butt everytime and I love it. Lots of sweat, power, and loud music. Its not quite the club but you get the idea.

I am 5'10", 303lbs with my ideal weight being in the neighborhood of 215-220. I am currently preparing for a tri in Oct. and wanted to avoid buying a cruiser if possible. I want to purchase a bike that I can compete with. Can you really compete in a tri on a hybrid? My apologizes if this seems like a naive question- just getting into the sport and trying to learn as much as possible.

I started at 315, and at the time, my opinion was that the type of bike didn't matter (and I still hold to that opinion). Buy the cheapest bike you can get away with - a beat up second hand craigslist mountain bike. Anticipate that if you use the bike, you will destroy it.

The flip side is that if you use it, you will likely lose weight. Because you'll have lost weight, you'll actually be in a position to take advantage of a higher quality bike, and your bike fit may change. So, you'll be ready to pull the trigger on a higher end bike, one that is actually good for competing.

This allows you to avoid a high cash outlay now, learn about what you like/don't like in a bike, familiarize yourself with technique (balance, braking, etc.), and get a higher quality bike when you'll actually be able to notice and take advantage of the higher quality. It will also give you time to see what other people use, demo other bikes at events, etc. All around a win-win, I figure.

Just my $0.02.

In my experience, the frame isn't really the issue with being overweight (unless you're thinking of a full carbon frame). It's the wheels that really matter. I don't know enough about wheels to suggest a specific wheel, but you should be able to find a million threads about wheels for overweight cyclists (check bikeforums.net if you can't find enough here).

Also, I'd definitely buy used. You can get a 5-year-old bike for 1/3 the price of a comparable new bike. I'd look for a nice aluminum bike that's a few years old, and you'll be able to get a lot of bang for the buck.