I do not care what anybody says about weight training and cycling. My personal experience is that my 3x a week weight training has made me a better athlete, which by extension, has translated into being a better cyclist. I keep my weight training sessions short, while hitting all the big muscle groups,and I also do a 30minute stepping session before the weights.
It just works for my stamina/endurance , recovery and overall fitness.
And I found out this routine works even better, the older I get.
I really think weight training (not weight lifting) is vastly underrated as a fitness component.