The lighter gravity matters only if they're pushing it down as opposed to leaning on it to hold it down, as if they're leaning on it, then the lighter gravity means their lean exerts a weaker force as well, also, generally leaning exerts a greater force than pushing.

Bassically for it not to fall the Dwnward force F (exerted by the bridgemen) multiplied by the distance z has to be equal to or greater than the weight of the bridge w multiplied by the distance x, where the distance x is the distance from the middle of the bridge to the edge of the plateau it's being pushed out from.

Let's say that the bridgemen lean on it to put half their weight on it and lets postulate that they weigh about 100 pounds, the bridge weighs 2000 pounds and is 30 foot long and they're trying to push it accross a 25 foot casm.

When the bridge touches the other side they'll have 5 foot of it left, and lets say their downward force is effectively a foot in from the edge meaning they have 4 foot of distance from downward force to edge of casm.

The bridge will currently have it's middle 10 foot out, thereby exerting a moment of 2000 pounds x 10 foot x g (where g is the appropriate gravitational constant) so, 20000g

If we divide 20000g by 4 we get 5000g, that would mean 50 bridge men exerting 100g each to stop it from falling as it reaches the other side.

Maybe they could lean a bit more, three quarters of their weight, 5000g/150g = 33 and a third bridge men, or 34 as we don't have thirds of men lying around.

Not sure how 34 bridge mena re going to crowd around it and manage to lean a third of their weight on the thing...

I'm thinking our casms are probably narrower.