If weight training helps your cycling - it mostly means you are a rotten cyclist.
If cycling helps weight lifting -same thing.........
My answers usually make an attempt at accuracy - and this one is no different.
However, with semantics and but without context these threads more often confuse than enlighten.
As one post points out - very knowledgeable people know how to use weight training to improve human performance.
However, without context - and without prioritization of a given athlete's status and stated goals much gibberish can be thought of as "correct."
In the end - as usual - my pithy comment is probably best. Alternative training does not improve "cycling" until an athlete exhausts all the avenues of training adaptations afforded through quite a bit of bicycle riding. I doubt this to be that case of the OP - but I digress.
My narrow perspective is worthless to most people.