I work my legs twice a week in the off season, once a week during the season. Studies have shown that once a week at lowered reps (2 sets of ~5, to failure) retains muscle cross section area at little cost in training load. Works for me.
During the season, I do half squats, down to a 90° knee angle or a bit lower. That's inside the range of motion on the bike and allows the use of heavier weights with a lesser risk of injury. I also do single leg presses, same range of motion, standing one-legged calf raises to full range of motion, and bent leg lifts on the Roman Chair bringing knees higher than hands. Single leg presses are particularly interesting because one can vary the load on the quads vs. hams and glutes by changing one's foot position on the board. Good for correcting weaknesses.
In the off season I add knee extensions from 150°-180° only and sometimes straight-legged deadlifts.
For me, weights increases the time I can spend overgeared on very steep hills and possibly the power I can put down there. There is no appropriate gear for spinning up 18% grades, at least for us mortals. As noted above, anytime one can spin, one gets no extra power by lifting weights, however I also believe it increases time to exhaustion at lower effort levels.
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Results matter