Using tbl_custom_summary, you can create this kind of table relatively easily:

library(gtsummary)
library(survey)
data(api)
tbl_custom_summary(apistrat %>% filter(cname %in% unique(cname)[1:5]),
                   include=c("stype", "cname"),
                   by=yr.rnd,
                   statistic = all_categorical() ~ "{mean}",
                   stat_fns = everything() ~ function(data, full_data, variable, ...) {
                     summarize(data, mean=Hmisc::wtd.mean(meals, weights=pw, na.rm=TRUE))
                   })