Is it normal to weigh more on my period?

Yes: Some women due as a result of water retention. Then as the hormones change that goes away. Most women do not see a significant change in weight.

Weight change: Yes this is normal and is due to water retention that is shed once you go through your cycle.

Yes: Women tend to retain some fluids around their periods. That's where bloating feeling comes from for example. Some extra weight may be attributed to water retention.