Two ways:
Your weight feeds your power-to-weight number: your FTP (functional threshold power, the hardest effort you can hold for about an hour) divided by your weight in kilograms. That's the number that decides how a climb feels. Two riders holding the same watts don't climb the same hill the same way if one is carrying ten more kilos. It cuts the other way too: dropping two kilos while holding the same FTP raises your power-to-weight just like adding watts would, and for most of us it's easier to find.
When you log a new weight, your power-to-weight on the Me Card updates to use it. RideTool shows the date of the weight it's using, so you always know how current the number is.
Daily weigh-ins bounce around. A liter of water is a kilogram. A big dinner, a long sweaty ride, a salty meal, each one can move the scale a kilo or two overnight without your body actually changing. That's noise, not progress or backsliding.
So don't sweat any single entry. Weigh at roughly the same time of day, log it, and look at the line over weeks. The trend is the real signal, and it moves slowly, the same way fitness does. You don't have to log every day either. A couple of entries a week is plenty to keep your power-to-weight honest.
Entries appear on the day you logged them, on both the week view and the calendar. And Claude can pull the whole history if you ask "show my weight trend", or answer questions like "how has my power-to-weight changed since spring?"