Do larger rockets tend to have a better mass ratio due to the square cube law? I mean, larger tanks have a better surface-to-volume ratio, so their weight-to-volume should be improved
It doesn't really work that way, because a tank isn't just a volume; the tank itself is a structural member that needs to support the mass of the material contained inside it (and in most cases the tank also partially supports the rocket itself, so add in the mass of the upper stages and the aerodynamic forces). A larger tank needs walls that are proportionally thicker to keep its structural integrity.
The walls of pressurized tanks in particular need to get thicker as the pressurized volume increases, so the tankage mass still increases pretty close to linearly with the tankage volume, and tankage is most of the mass of an orbital launcher.
Larger rockets do still have a few scaling advantages. Avionics doesn't scale up with rocket size; cable runs scale 1-dimensionally; aerodynamic drag is generally proportional to cross section and to surface area rather than to volume, etc.
Unfortunately, it works the other way around: Structural stability requirements grow with the mass and hence the volume and hence the cube of the linear size, while the means for stability are cross-sections of structures and hence only grow with the square.
At some point, like the large dinosaurs, a rocket would not even be able to stand, let alone accelerate and withstand dynamic loads. (This is the primary reason we don't have space elevator towers.)
The main advantage of larger rockets is a lower air resistance per mass, which probably means that very small rockets have a disadvantage in the atmospheric phase of the ascent.