Since you're already comfy at 60 pounds, get yourself a bow that draws 60 pounds at the low end of it's draw weight range. Try to shoot every other day. It's very important to allow your muscles a day of rest between sessions or you will impede your progress. Shooting only once a week or less will also impede your progress.

So, we'll assume you'll shoot every other day. Once a week, increase the draw weight by a half turn on the limb bolts. That lets your muscles adapt slowly and, unlike weight lifting, you'll be strengthening the specific muscles and supporting muscles you'll be using to shoot.

You'll be shooting 70 pounds within a couple months and likely won't ever notice the weight increase - except for probably needing stiffer spined arrows at some point.

And definitely concentrate on using those back muscles instead of the arms!