You have basically three issues to deal with here.
Extra baggage
Oversize
Overweight
Eliminating as many of those issues as you can increases your odds of getting the bike fee reduced or eliminated. The good quality hard bike cases are going to put you over 50 lbs. Just about any bike case is going to be oversize unless it's a bag or a homemade box. If you're traveling in the US it might make more sense to ship the bike via a ground carrier than take it on the plane.
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