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llinllinn, welcome to the BA forum and please to continue to post here. There may be ways to help you here, so FT is the right place to raise this point. Welcome on board.
For example if you get status with BA then you are allowed an extra bag and a heavier weight limit. And it could be status with another
oneworld airline such as Qatar too. If you are not a regular traveller then this isn't so easy to get, but if this travel is the start of a regular process then you may want to do some research as to whether you try to get status for future travel
Also, rather than paying extra for a bag, you may want to consider spending the money on World Traveller Plus (premium economy) since that also gives you another bag.
More details here:
http://www.britishairways.com/en-gb/...age-allowances
You could also consider getting a cheap bag for the return leg if you are only using the bag in one direction. Ikea's zip bags have been used in extremis!
BA's charges are a lot more reasonable and generous compared to some airlines (e.g. Cathay Pacific) and their allowances are at least as good as the rest of the pack in this area.
And regulars will see this coming: unless you are moving house, it's perfectly possible to live off hand baggage with a bit of planning and careful packaging. I survive for weeks of travelling off a single carry on bag - I don't check in a bag at all.