Yes, it is very rude and intrusive for men to look women up and down.

You seem preoccupied with food, body size and weight and you assign motive and meaning around these factors. Not everyone has these same preoccupations. It is entirely possible that her discomfort is nothing to do with self-consciousness about her own body size, but rather that being looked up and down is a dehumanizing and objectifying experience for all women regardless of weight.

You don't need to make eye contact, but you need to establish a way of interacting with women which doesn't involve looking over our bodies whilst disregarding our faces. Maybe she can help you with the social convention and expectation stuff.