I had this issue recently, on a 016 ticket, EWR-BRU, then BRU-ZRH-EWR.

The Swiss baggage allowance was all over the place.

United said 1 bag, 50 lbs.
Swiss e-ticket said 1st bag 50 lbs free, 2nd bag 70 lbs.
Swiss CS (three different times) said 2 bags, 50 lb each.

However, the e-ticket also did say I could not buy extra baggage because another carrier had the baggage decision.

I ended up packing 2 bags at 50, 1 at 70. At check-in at the airport, come to find all three at 70 would have been fine.

Native Swiss flight number.