The OP's question is in regard to international flights.
I'm flying the following itinerary in September:
- EWR-LHR
- LHR-NBO
- NBO-LHR
- LHR-EWR
If I had just booked the inner pair my baggage limit would be 23 kg total. Since my itinerary is "to, from or via" North America, I am allowed to check 64 kg -- more than twice the luggage -- on each leg.
Even if the itinerary was reversed -- NBO to EWR via LHR -- I'd be able to pack more than the First Class NBO-LHR passenger.