Correct. A higher index means less curvature is needed to make the prescription, which means thinner (and therefor lighter) lenses. That said, for weak prescriptions, the difference is so small as to be immaterial.
What is material is that the polycarbonate lenses are harder to scratch.
FWIW, I have such a strong prescription that I have 1.7something high-index lenses to keep them light. I also have premium anti-reflective/anti-scratch/dirt-repellent coating. All in all, they're $500 lenses. It's also time for new ones, it's been about 4 years!