Biexciton binding in GaAs quantum wells has been investigated for a range of well thicknesses (80-160 Angstrom) with spectrally resolved photoluminescence and transient degenerate four-wave mixing. Both light and heavy hole biexcitons are observed. The ratio of the binding energy of the heavy hole biexciton to that of the heavy hole exciton is found to be approximate to 0.2, and nearly independent of well width over the investigated range. A new theoretical calculation agrees very well with the experimental ratio. This ratio is larger than predicted by Hayne's rule for three-dimensional biexcitons.