Yes, it does. You wouldn't use it for height, though. You could say 'I'm tall, just like my mum'. Or you could say 'I'm the same height as my mum'. (or 'nearly' or 'about the same height') 'Weight' can change (obviously!) , but you could say 'I have my mum's figure', if your body shape is the same.

Yes, it means you inherited your eyes from your mother, so yours and hers look similar. You can also use this phrasing for other body features. It's possible to say you have her height if you are fully grown, but as for weight it makes more sense to say "my mom's build" or "my mom's physique". Weight depends partly on lifestyle as well as genetics.

I have my mom's eyes............................... I keep them in a little box in the refrigerator. I'm only joking!