Composite weight using values from 2 tables.

Somewhat complex challenge you got there. Try this measure, I am not sure I got all your conditions right, if not let me know and I'll rework:

CompositeWeight = 
VAR AWeight = SUM(TableA[Weight])
VAR ACountry = MAX(TableA[Country])
VAR Prod = MAX(TableA[Product])
VAR NoResponsesCountry = COUNTROWS(FILTER(TableB, TableB[Product] = Prod && TableB[Response Recieved?] = "Y" && ACountry = TableB[Country]))
VAR NoResponses = COUNTROWS(FILTER(TableB, TableB[Response Recieved?] = "Y" && ACountry = TableB[Country]))
VAR Props = DIVIDE(NoResponsesCountry, NoResponses)
VAR X = LEFT(MAX(TableA[Product]), 1) = "X"
RETURN
    IF(X, DIVIDE(AWeight, Props),1)

I am assuming here that you would use this in a visual with at least Product and Country as row contexts. I'm using a lot of variables in order to explain, no need for all of that in your work product of course.