I'm hoping to go with BA. They can cost a little more and you can pay for extra bags. This is from their website. Just remember all flights must be BA - no code shares!
If you wish to take more bags than your free checked baggage allowance, you can pay to check in up to 10 extra bags per person with the same weight restrictions as your free allowance.
Extra bag charges when you pay in advance on ba.com.
Cabin Free allowance 1st extrabag Further extra bags
First
Club World
Biz Bed 3 bags £77/$119/€98 £77/$119/€98
World Traveller Plus
Prem Plus 2 bags £77/$119/€98 £77/$119/€98
World Traveller Y class
(full-fare Economy) 2 bags £77/$119/€98 N£77/$119/€98
World Traveller
Eco 1 bag* £34/$51/€43* £77/$119/€98
Club Europe 2 bags £34/$51/€43 £34/$51/€43f
Euro Traveller
UK Domestic 1 bag £34/$51/€43 £34/$51/€43
Euro Traveller
UK Domestic
(hand baggage only fares) 0 bags £20/$30/€25 £34/$51/€43
* Some Frequent Flyer members have a free checked allowance of 2 bags, please refer to the section above for more detail (Size and weight of free baggage allowances) Customers travelling to and from Brazil, Ghana, Kenya, Liberia, Nigeria, Sierra Leone and on connecting journeys between India and USA/Bermuda/Canada have a free checked bag allowance of 2 bags. Extra bags will be charged at £77/$119/€98 per bag.
Charges are shown in UK pounds, US dollars and euros.
Charges in euros may vary depending on current exchange rates.
Charges will be converted to local currency at the airport.
You cannot purchase extra bags for an infant, under 2 years of age.
Pay for extra baggage using Manage My Booking