Complex sum function

I have a spreadsheet with 3 tabs:

• Tab A: The first column is a list of numbered milestones, with one milestone per row. The subsequent columns are weeks in the year. There is an x in any column when that milestone will take place (e.g. Milestone 1 has an X in the columns labeled 3/10 and 3/17). Multiple milestones take place during the same weeks (e.g. in 3/17, there may be X's in the rows for Milestone 3, 7, and 9).
• Tab B: The first column has the same list of numbered milestones. The subsequent columns are labeled with staff member names. There are numbers of hours listed by staff member and milestone (e.g. John will need 10 hours to complete milestone 1, so there is a 10 in the Milestone 1 row under his name). Each staff member may have hours attached to a variety of milestones (e.g. John has hours in the rows corresponding to Milestone 1, 6, and 12).
• Tab C: The first column is the same list of staff members that head the columns in Tab B. The subsequent columns are labeled with the same list of weeks in the year as in Tab A.

Essentially, I want to know how many hours each staff member is assigned in a given week, based on the milestones they're assigned to and the timeline for each milestone. For each individual staff member, I need to sum any hours associated with a given milestone, but only if it takes place in the relevant week.

How should I approach this?