Does an object float more or less with more or less gravity?

The object would actually float exactly the same for both values of $g$. Let $V$ be the volume of the body, $d$ its relative density, and $V'$ be the volume inside water. Then for equilibrium of the body,

$V \cdot d \cdot g=V' \cdot 1 \cdot g$

So, $V'/V$ is independent of acceleration due to gravity.

If your object is compressible, like wood, it definitely might not float at higher gravity. The higher pressure in both the water and the air might compress the object to the point that its density exceeds the density of the water (which is much less compressible than spongy things like wood). This is an important plot point in the classic science fiction novel Mission of Gravity by Hal Clement.

I generally agree with Amritansh Singhal's answer and Yakk's comment, but I would like to add that in some situations there is another mechanism of floating that significantly depends on the value of g. For example, water striders (https://en.wikipedia.org/wiki/Gerridae) walk on water using surface tension to prevent sinking. In this case, higher g would make their life harder:-)