Sure the vertical force on the tires is the same when standing still, but what about the force required to stop 342kg vs 900kg of inertia if you hit a large pointy rock at 1m/s?
That's what's referred to as dynamic acceleration. Rolling along at 1 m/s and then coming to a sudden stop by running into a rock would indeed produce some big accelerations, and the difference in mass between Curiosity and Scarecrow would be pretty significant.
However, the scenario that you and an earlier comment are talking about - coming to an abrupt, rocky stop from 1 m/s - simply does not happen. You might be envisioning Curiosity as some sort of Martian ATV bouncing off the landscape and doing power slides, but the reality is far more prosaic. Curiosity's top speed on flat, hard soil is about 0.04 m/s, not 1 m/s. Let's say that, for whatever reason, Curiosity came to a dead stop from it's top speed in, say, 100 ms (the suspension ensures the stop is not instantaneous). That's an acceleration of 0.4 m/s^2. The static acceleration due to gravity on Mars is 3.7 m/s^2, or about 10x that.
In other words, the dynamic loading is going to be small compared to the static loading.
What is more: Curiosity has about a dozen people planning out its path, specifically to avoid running into things. Even beyond that: Curiosity has hazard avoidance cameras and autonomous algorithms that will slow or stop it before it hits anything.