Create "snapshots" on changing data

Power BI does not have incremental load at present. This means that if you try to timestamp something at the time of query load, you will get updated values for the timestamp when it is refreshed. You might be able to hack around this but I can't think of a creative way at present.

One solution might be to pull each week's data in as a separate table and have a custom column either in M or DAX that puts in today's date. Load the data, which will populate the field and then disable load and refresh for that query. You would create a new query every week by essentially copying the query, pull the data, disable load and refresh.

Then, you would have an append query that appended all of these separate tables into a single table. In this way, you would have what you want, albeit, with a bit of manual work each week to create the new query and add it to the Append query but that's like 15 minutes of work each week really.