John Long asserted back in the 80s that the fear of muscle mass was unfounded - he estimated that most climbers could increase their strength by 20% for a 5 pound increase in bodyweight. Few people listened.
I'm 6'1" and a much better climber at 190-200 lbs than at 160 lbs. Get your deadlift up and then (only afterward!) think of the hangboard as a conditioning tool for your grip, rather than a strength tool.