Nearing the end of When the Moon Hits Your Eye by John Scalzi, which came out a few months ago. It's a bit silly but I'd recommend it. The premise can be summed up as, "What would happen if the moon turned into cheese?"
At 8 deg C, mean densities of blockformed and conventionally-hooped cheeses were, resp., 1.094 and 1.091 g/ml.
So that's 1094 kg/m³.
Basically, Earth's tides would be about a third as strong, which I imagine would affect a bunch of things, especially coastal ecology. Dunno how much tides affect weather.
Also, probably alters the reflectivity of the Moon, so would affect the brightness of the Moon. Might affect a lot of nocturnal critters and such. Hard to estimate, since that depends a lot on what cheese is involved.