here are some excerpts from "Flight Theory for Pilots" byCharles E. Dole:
"When an aircraft is in steady flight, horizontally, the lift is equal to the weight of the aircraft. "...,shows that the lift is less than the weight if the aircraft is in a climb. this is possible because some of the thrust supports some of the weight of the aircraft. The steeper the climb, the less the lift supports the weight."
"The velocity for for maximum rate of climb cannot be determined by a simple examination of the Ta-Tr curves.. RC depends upon velocity and excess thrust, both of which are variables."