Weights are fine, and at lot of coaches and top athletes advocate them BUT it can never be a ride replacement, and a proper weights schedule would see you coming to the end of your cycle fairly soon, at least for the legs. A proper schedule will see you doing about 10-12+ weeks of Adaptation, hypertrophy, strength then power. Hitting the weights with not structure will do more harm than good, it is NOT about the most you can push.
We had a guy on the team hit the squat rack hard the day before a big training ride - the result? He flagged big time, and wasn't able to get the most out of the ride on the climbs etc. He then had to miss the next day as well to recover. He won't be touching the squat rack again.
I started off keen to do weights this year, but I am very time constrained, so weights have gone out the window and been replaced with on the bike stuff.