t test for group difference if data is paired in some cases (repeated measurements) I like to test if mean differences between overweight and normal weight subjects is zero. Since the data is longitudinal (subjects measured several times) and my outcome is in percent (continous variable), I am struggeling which statistical test to apply. In the cross-sectional case I would apply a t-test/Welch test. For the longitudinal case I read that fixed effect regression is an alternative. As far as I understood, the subjects will be entered as Dummy-variables in the model but I am not sure if this is useful because I do have many subjects (around 700). Furthermore, my outcome is in percentage. Does this mean, I need to use fixed effects beta regression?
Is it possible to use the t-test/Welch test although weight status of one subject may vary(from overweight to normal weight or the other way round)?
I highly appreciate any help :)

The usual way to model "longitudinal" data, i.e. data with subsequent multiple measurements on the same items/persons, are mixed models. The item/person id is treated as a "random effect" and the effect of interest as a "fixed effect". In your case the group membership would be the "fixed effect" predictor, and you can apply significance testing on the predictor.
This seems to be problematic in your case, though, because (if I understand your explanation correctly) the group membership is not an independent variable, but actually a response variable that changes over time depending on other predictors.
