Why can I not connect Health on the web?

Apple Health and Health Connect connections need the mobile store app. A browser cannot access those phone health services, so the web version cannot establish a connection or change its Health permissions.

Open Calsa on your phone to connect and select what to share. Values brought into the same account by that app can then appear on the web with their source and latest time. You can enter weight manually on the web if you do not want a phone connection.