I have time series and would like to have weeks based on date I got. I used Date&Time to String node with date format w which is ok if a time series is not longer than one year. In this case first seven rows are 1, second seven rows are 2, etc. If it is longer I would like to continue counting weeks. So to get 53,54,55…

You can use the Date&Time Difference node to calculate the $Difference$ between each of your dates and the minimum date, measured in days. Then you can use a Math Formula node: floor($Difference$/7).