I had a big discussion on this in the cyclingplus forums. Basically it sounds like strength has little effect on cycling. It is a weight supported exercise, and those who weight lift during the winter find that they lose most of their muscle in the cycling season. It is primarily aerobic strength that is needed.
While I believe this is all very true, I weightlift, mostly because I have a gym membership that I like to take advantage of. I work on my upper body, and hamstrings. I haven't seen any visible effect on my cycling from this, and if you're a spinner I think you'd see even less benefit.



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. We carry way more body fat quite naturally, and it takes longer to convert that to muscle. Last year I wasn't riding much, and certainly not miore than 20k at a time. But I did start weight training, mostly because I kept getting a sore back on the bike, and my chiropractor said I had no core strength, and my back muscles were (quote) "that of a sedentary office worker - just pathetic". So off I went to the gym, got a personal trainer to guide me in and show me how, and wow, what a difference! I don't weigh any less, but my shape has certainly changed. I have toned biceps, triceps like nuggets, good core strength (still working hard on this, and am starting Pilates next week to get it better) and my back has never been so straight and strong. I now ride 100k+ just about every weekend with no back issues - my major problem is running out of breath on hills! So that's my next project. Oh, and trying to get the extra fat off my legs and tummy so I can see the great muscles I know are hiding underneath there! As a bonus, because I'm over 50, I'm also staving off osteoporosis. Being strong and feeling strong is soo good, and for me, it does help with the cycling.