Actually, going with a 1/2" dia. eye bolt for your anticipated load of 150 lb. would be similar to using a howitzer to shoot a mosquito. It will work, but why such overkill??
You could easily get by using a 3/8" dia., which for a Grade 2 bolt (weakest grade available) would have a working (proof) load of 5750 lb. in tension. That's a factor of safety of 5750 divided by 150, or 38 times stronger than you actually require. Unless your exercise program is going to beef up your total muscle structure to astronomical proportions, don't bother with the 1/2" dia. eyebolt.