Student or Learner
"I've been working out a lot and garduated to lifting 80 lbs."
"I've been working out a lot and made my way up to lifting 80 lbs."
Yes, both sound OK, although graduated sounds a little odd. I understand that you want to emphasis the "achievement" of it, but as 80lbs isn't really an "end-point" I'm not sure it's the best choice of word - what would you then say when you reach 85lbs?
I think I might say "I've been working out a lot and worked my way up to lifting 80lbs." rather than "made my way" but then that leaves a rather ugly sentence with two forms of the "work" in it.