Usually, hCG levels off at 6,000 mIU/ml. From this moment on, it is expected to double every four days (keep in mind that, at the beginning, it doubles every 48 hours). The production of hCG is expected to stop rising around week 8-11 of pregnancy.
Some experts believe that the reason why hCG levels stop rising at this point is because the placenta starts making estrogen and progesterone from this moment on. In other words, that hCG is no longer necessary to stimulate the ovary, which was responsible for the secretion of these hormones up until that point.