Warping:
Basswood is a very soft wood, that is what makes it wonderful to cut in a laser. You can cut it fast! But because of the lower rigidity, thinner basswood, especially 1/16th and 1/8th have a tendency to warp.
What causes warping? Short answer: humidity changes. Changes in moisture content of wood causes it to expand and contract, ever so slightly. If the layers expand or contract unevenly then the boards can warp.
What can be done to minimize this problem? Store the material flat, preferable with a weight on them to keep in a flat position.
What can I do to correct warped boards? If the wood is only slightly warped, use pins or tape to flatten the wood. If this is not sufficient, then spritz both sides of the boards with water or use a damp cloth to gently dampen both sides of the boards. Then place on a flat surface with weights on top forcing the boards into a flat position. As the wood dries over several hours to a day, it will dry flat.