Understanding Society User Support

As part of my analysis, I am conducting three lagged general linear models on Youth and Adult surveys. In each model, I regress a variable from Wave 3 of the Youth survey onto a variable from Wave 6, 9 and 13 of the Adult survey, respectively. Prior to the models, I filter all the Adult waves to only contain respondents who have responded in Wave 3 of the Youth survey.

I wasn't able to find information on how lagging variables from these two surveys should be handled. Should the cross-sectional or the longitudinal weight be used? If the latter, should it be the longitudinal weight specific to the wave used, or the very last wave that's being analysed, considering three separate models?