In longitudinal regression(ex: repeated measures for different people), we have the option to choose a correlation structure for the response variable. For example (https://youtu.be/qoqhPq_VILc?si=yJmlrWR4hlgOz1IL):

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But is it ever possible to have these kinds of correlation structures for the independent variables? I suspect that in many scenarios, the independent variables (covariates) are also correlated for the same subject from measurement to measurement.

For example, in geriatric overweight patients, the patient weight (kilograms) almost always increases from measurement to measurement for the same patient (ie correlated). Thus, for the same patient, the weight variable is not IID .... which can be a violation of assumptions.

Is there any modelling approach I can use for longitudinal regression (repeated measures) when I suspect that the independent variables have some correlation? Can I specify a correlation structure as well?