According to the EK website, this will help things go smoothly
8. Can excess baggage allowances be pre-purchased for an Emirates flight?
Excess baggage allowances can be pre-purchased to avoid time spent at the airport on departure ONLY if you know the excess weight in advance.
Purchases can be made from your local Emirates office. Charges will be according to the excess baggage weight and the destination.
I assume you are flying on 1 ticket? If not, the excess charges will be a lot more. The allowance is only 20kg per person on EK flights when baggage is not checked through and excess rates are quite expensive ($10 / kilo approx) so 50kg would be around $500. Showing them your ticket to/from IAD might worked. It has worked about 60% of the time in my favour.
Cheers