From its beginning, the measurement of optical rotation (OR) is crucial for the analysis of chiral molecules in many fields. However, the precision measurement of a weak OR signal with conventional setup remains elusive. In this Letter, we experimentally propose a precision method to determine the OR of glucose and fructose based on weak measurements. By using the spin Hall effect of light (SHEL) as a probe, a nonlinear weak measurements model is established that is applicable beyond the Aharonov-Albert-Vaidman (AAV) limit. Due to the high sensitivity of weak measurements amplification with respect to the OR, a tremendous variation of the amplified beam displacement of the SHEL is observed, while the concentration of glucose and fructose is slightly changed.