AFAIK: On through-checked baggage, US Department of Transportation regulations require the marketing carrier of the initial segment baggage rules apply to USA originating (or ending, iirc) flights. E.g. flying AA as your first flight, AA rules should apply. These take precedent of IATA rules if travel begins (or ends) in the USA.

For IATA governed international itineraries, baggage rules of the Most Significant / Prevailing Carrier apply (in your case, that would be Iberia, as the MSC transatlantic carrier, if they weren’t superseded by the USDOT regulations).