I have and use weekly notes now; I used to do monthly as well but found it confusing (mapping weeks into months isn’t clean). Also found that I seem to work on weekly cycles for planning and daily for execution, so ¯_(ツ)_/¯
For the Daily note format, I use YYYY.MM.DD-WW.dd, which gives me 2020.11.09-46.Mo for daily note names (week number is after the dash). On a Monday, I create the daily note as usual and then duplicate the file, and just trim the .Mo from the filename giving me 2020.11.09-46 (week 46, starting on the 9th of November). I also find it convenient to see what happened on Wednesday of week 42, for example. So my daily notes folder looks like this:

Easy to see the week notes, and also easy to bring up both the week notes and the day notes for that week:

Not a standard by any means, but after trying various standards-based formats I’ve settled on this - it works well for me.