In my experience, all our student were weighed, as were we instructors, and a complete W&B was conducted regularly during flight training. We had some heavier machines that were impractical for a heavy student and instructor, a couple with odd CofG locations that required higher than normal minimum fuels to remain within limits, and other restrictions. A student who couldn't provide the correct details in a preflight brief didn't fly.
With regard to heavier pilots, not everyone fits in the little machines and if you still want to do the training then paying for a larger machine is sometimes the only legal or practical alternative. Breaking the rules isn't.