Carrying your equipment on the plane with you can result in unnecessary charges. The person behind the counter has probably been working a hard day of dealing with rude and tired travelers, so its best to avoid any inclination that your baggage should be charged.
From AA website on the date of this post:
For flights wholly within the United States and between the United States and Canada the maximum amount of baggage each ticketed passenger is allowed free of charge is:
2 pieces checked and one carry-on
Please note that one carry-on personal item (see "Carry-on Allowance") does not count toward the free bag allowance.
Size and Weight
The size limitation of your luggage is calculated by adding the total outside dimensions of each bag, that is, length + width + height.
Two checked bags at 62 in/157 cm each
One carry-on bag at 45 in/114 cm
The maximum weight per checked bag is 50 lbs/23 kgs.
The maximum weight per carry-on bag is 40 lbs/18 kgs.
Excess charges always apply to the following sports items:
-Bicycle (if exceeding 50 lbs/32kgs or 62 in/157cm)
-Scuba Tank (empty)
-Wind surfing equipment
-Hang gliding equipment
The following items are free in place of one of the 62in/157cm bags within the free baggage allowance:
-Bicycle (if within 50 lbs/32 kgs and 62 in/157 cm)
-Bowling equipment (bowling case with up to three bowling balls and shoes)
-Fishing equipment (2 rods, reel, net, tackle box and 1 pair of boots)
-Golf equipment (1 bag, 14 clubs, 12 balls and 1 pair of shoes contained in a self-provided travel bag or box) is not subject to the $25 charge for baggage weighing over 50lbs. but no more than 70lbs
-Ski equipment (1 pair of skis, poles, boots, and bindings. These items will count as 1 item.)
The best way to get around this is to pack your kiteboard separately in its own bag. It will be longer than the dimensions allowed, but should fit as a substitute to one of the checked items provided you convince them that its not windsurfing equipment or a surfboard. Most check-in personnel have no idea what a knee board is, so you can say its a "knee board" or a "snowboard". Obviously, you're going to have to act confident of this and convince the person that, if they ask, you are telling the truth. They are just itching to charge you.
By packing the kiteboard separately, though, you will most likely avoid any attention to the bag in the first place. Since you're taking a vacation to kitesurf, you will most likely be going somewhere there's wind, and plenty of it. So you don't need a huge board. Take a board that is no longer than ~155cm. Its packed-dimensions will be relatively short and light, since its only the board, and the person checking it will probably not even bother to measure it. If its within the limits, or at least considered to be, it can be anything you want.
Then for your harness, kite, controlbar, etc, you can use a large duffel for hockey equipment to pack your clothes and shoes, and your kites and kitegear. If your girlfriend is going, the two of you have 4 check-ins total, with each having a carry-on and a personal carry-on, making 8 bags total. That's plenty for 3-4 kites, two boards, wetsuits, etc. One hockey bag will get all the gear into it and you can shoe both boards into one boardbag and then use her two check-ins to pack all the clothes and stuff.
If you go with a board+kite bag, bigger and thicker and heavier with all the added equipment, you'll raise eyebrows. You can pull it off, and maybe they won't even look, but the risk is going to increase the larger the bag becomes. A hockey duffel is something they see a lot and would pass pretty easily.