Assuming your membership table has a linked records field tying it to the payroll table, I would think you could do this through a roll-up. Create a new field in your membership table and define it as a roll-up field using the SUM() function on the weekly dues field. That should bring the total paid per member over to your membership table, where it could be used to calculate amount owed.
However, from your description it sounds as if your tables may be ‘soft linked’ – that is, each table has a field based on common data (employee ID), but aren’t explicitly linked. If so, you’ll need to hard link the tables through a linked records field. This is easily done; there’s a short video tutorial in the Airtable support entry on linked records fields that tells how.