<shy>
Is it "normal" to have difficulty pulling a 60lb draw?
Normal is a wide spectrum. The middle range of men in the bow drawing spectrum will handle 60 lbs. while one end of the normal human range will have a LOT of trouble with that draw weight and a comparable few on the other end will draw it with hardly any effort. FWIW when I started bow hunting, 60 lbs. was considered "heavy" for a recurve.
Your question took guts. You may achieve 60 lbs. if conditioning your muscles is the problem, but you may need to go to a lower draw weight. We used to kill deer easily with 45 lb. recurves, and a friend of mine shot an arrow clean through a huge javalina with a 33 lb. recurve.
It would help if you got a bow expert to isolate what is giving you trouble. There are several possible factors: Natural muscle strength, conditioning of those muscles, physiology of skeletal and musculature, technique, equipment, or some combination or other factor. I have members of my extended family with exceptional strength -- and members so far on the weak end of the core muscle spectrum that they needed physiotherapy as children to learn to walk normally.
Grizzly bears are built stronger than black bears, etc. You can condition and build muscle, and you may have to work at that more than others, but a lighter draw weight may serve better. If you struggle to draw you won't shoot as well. Technique may help if your physical structure is a problem.
Figure it out and go for it.