David,
If I can make a suggestion, I would recommend that you buy "The Cyclist's Training Bible" by Joe Friel and read it. Twice. I've read a bunch of the threads on this list about the use of weights in cycling, and I'm frankly unimpressed; people are so entrenched in who's right and who's wrong, that study results are interpreted and reinterpreted to suit each side's point, and any worthwhile information is lost in the war of words.
From your post it sounds as though you are interested in racing bicycles and want to know how you can get better at it. Cutting through all the **** here about whether weights help or harm cyclists, whether you can gauge fitness without a power meter, or whether or not you're getting enough protein in your diet, you first need to understand the specific demands of bike racing. Friel does a good job laying out (with plenty of references for those of you demanding scientific proof) the specific demands of different types of races (RR, crits, TT, stage races, euro vs american style races, etc.) and follows with a well-designed plan to help you assess your strengths and weaknesses, then lay out both short and long term plans to address them as they relate to the type of racing you're likely to be doing. From my own experience (all I have, lacking fancy degrees and credentials), I increased my average pace for a 30-40 mile solo ride from 15-16 to 19-20 mph in three months following his guidelines (something I'd been unable to do in any of my previous 15 years of riding.) For what it's worth, he advocates a weight regimen as part of an overall training plan, but generally limits this to early season (November - February, here in NH, USA.) He is an advocate of power meters, but works with HRMs for those unable to afford or justify the cost. I'd be happy to fill in a little more about the program, although I freely admit the ideas are not mine; they are simply the principles I learned reading his book and from subsequent informal study.