Clearly, there are plenty of cyclists between 200 and 250 lbs that get by just fine on whatever they're riding; they're not, however, riding on Fuji Team Super Lites, with titanium-spindled pedals and sub-100g stems.
The good news is that most of the really light stuff ships with rider weight limits. Those numbers may or may not be perfectly accurate, but they give you an idea of what you're dealing with.
Beyond that, if you're above average in weight, you need to use a little common sense is all. To be safe, don't buy components on the lowest end of the weight range for that category -- for instance, try to avoid stems which flirt with sub-120g figures. Avoid seatposts lighter than, say, 170g or so. Don't buy a set of handlebars which dip below 200 or 210g. The lightest stuff costs a pretty penny anyways; most of the reasonable gear is spec'd for better weight bearing.
You'll get the idea. Good luck.