I'm quite surprised that BD says the CO policy defines this one; generally the operating carrier's policy is the rule at play. If it is CO policies for TATL travel then it should be the 1x50# bag free policy.
For the EWR-CLE and CLE-LGA segments the rule is the CO domestic segment rule, which is no free bags for non-elites.
JFK-CAI-DAM will be the MS rules.