Question
whats the best way to keep the plastic on the ground when it gets windy during solarization?

Answer
Clemson Extension Service seals this deal thusly:

'Dig a trench approximately 6 to 8 inches deep and wide around the perimeter of the plot.  The trench will be used to bury the edges of the plastic to be placed over the plot.'  After soaking the Soil to break dormancy of Weed seeds, 'Cover the soil with clear UV stabilized plastic (polyethylene or PVC), and bury the edges in the trench. Stretch the plastic as tightly as possible. Once the plastic is in place, refill the trench, covering and sealing the plastic edges. This will ensure that the plastic is held in place and will prevent heat from escaping or allowing wind to get beneath.'

As a final measure, they say, 'Bricks or stones can be used to further protect the edges against wind or other disturbance.'

Doubling up on the plastic cover boosts your results: 'An air gap should be created between the two layers of plastic giving extra insulation. This air gap can be maintained by placing objects such as empty soda pop cans between the layers of plastic.'  And the hotter, and the longer, the better.

Good luck.  Keep me posted on how it goes.