I made sure the 4 bolts I've got holding the wood to the tire stick up high enough to prevent the weight from sliding off (in any direction). Plus, it helps that the plates I have at home have rubber around the edges, and the rubber against that wood doesn't let it slide much.
I've given it a few test runs in the backyard and the weight barely moves. That might change when I progress enough to stack weights on top of the 45. I may add a post in the middle when that time gets here.
During my test run, I was surprised at how much friction there was from the tire to the ground. There was a lot more natural drag resistance than I expected. Like Martha says, "it's a good thing."