Strength training is designed to focus on very specific muscle groups. Hence, technique is critical. In that regard it is like swimming, golf, gymnastics, etc; that careful precise ‘form’ will bring significant benefits to performance. Body weight alone will enable this, ie, no gym weights.
As just one example most athletes don’t do a Squat properly, and as a consequence, they actually exercise the wrong muscle groups and hence lack the benefits. This applies to many of the weight orientated Gyms.
There is also much discussion about the use of increasing weight vs increasing reps? Not dissimilar to the discussion here about Sweet Spot vs Traditional Periodisation, using higher volume low intensity.
The latter has implications for the type of cycling you intend to do. All out sprinters (in any sport) need large explosive muscles, and heavy weights help, endurance athletes, don’t want that muscle mass, so lower weights and higher reps are appropriate.
Regarding the squat, here is an easy test, that relies only on body weight:
Face a wall with arms crossed across your chest, feet just wide of your shoulder width, toes slightly pointing out; now squat looking directly at the wall, move closer to the wall, and repeat. Continue getting a little closer to the wall, see how close you can get, your target is your toes touching the wall, but if you get to about 100mm with your nose just touching the wall, you are doing very much better than most.
The point with this test, is that to do it, you need to have minimal ankle movement, ie, your shins stay fairly upright, and the main rotation is the knees and hips, with an upright torso. Most will not have the musculature to do this without falling backwards even with all their weight and concentration on their heals. Hence, body weight alone will develop that musculature, ie, develop that strength.
The Squat is a vertical exercise. The Romanian Dead Lift, (RDL) is a horizontal exercise. I mention this as many think they are doing a squat when they do their version of a RDL. In the RDL although the knee joint is slightly relaxed (not locked) there is virtually no knee rotation, unlike the Squat the main rotation in in the ankle and hips, the butt moves back as the hips rotate to allow the shoulders to lower, as the torso rises the butt moves forward - great for the lower back, ie, holding an aero position. Test: stand with your back to a wall, see how far you get away ie, progress, from the wall, as you push your butt back to touch the wall.