If this is all on one e-ticket (not PNR or booking), US law provides that the base travel allowance of the marketing carrier of the first segment, applies to all segments of the same ticket. Thus, IB's allowance will apply to the entire ticket. If two tickets, then IB to the first ticket and BA to the second.

This rule applies only to the base allowance and not to any waivers for status and the like.

Within OW, the agent at baggage check will see the allowance pop up, even if marketed by a different carrier.