As a previous poster noted, a main cabin fare is entitled to one free 50 lb./23 kg. bag on flights to/from Europe. There's a baggage fee estimator at https://www.delta.com/us/en/baggage/overview. The DL Amex card doesn't actually matter. Aside from the fact that it doesn't apply to non-DL flights, it's not an additional bag benefit (except for Silver Medallions on domestic flights). It's only a first bag free benefit and won't give you an additional checked bag when you already get one for free.