More copper in the board, means more lateral heat spreading in the presence of convection losses.
That is, consider a circular heat source in the middle of the board, and some rate of convection per exposed board area. In the first incremental circle around the source, very little heat is dissipated (small area), and heat spreads out at about the same temperature. Further out, some dissipative area has tallied up, and temperature starts dropping. Further still, temperature is dropping rapidly with radius, and additional area has little dissipative value. The solution for this scenario, with circular symmetry, linear conductivity, and linear convection, is a Bessel function, with the radial cutoff, within some margin of temperature rise, depending on the ratio of lateral conductivity to convection. Likewise, more conductivity, and a larger initial heat source spot, results in lower overall temp rise.
Real convection isn't linear, but depends on direction and orientation, and accelerates with temperature; for modest temp rise applications in random orientations, we expect this to mostly factor out, and amount to a manageable error (say 10 or 20% -- good enough for most thermal engineering purposes).
In all, typical heat-spreading distance for 2oz PCB is an inch or two, and the corresponding power dissipation at commercial ratings, about 5W dissipation capacity. Say for a D2PAK source.
If we have a major heat source (say, a power converter) in the middle of a board, and the board is more than a few inches across, we won't gain much from the extra area at 1oz, maybe 2oz, but we could increase copper weight to 3 or 4oz, or add planes (and pour signal layers -- total weight is what matters), to take advantage. We would evaluate the compromise between board cost and hardware (adding heatsinks or spreaders).
Conversely, if the heat source isn't too bad (a few W), we can consider shrinking the board outline, assuming we have the freedom to do so (given mechanical constraints e.g. fixed mount points inside a standard enclosure).
Notice I haven't given the equation / solution; this is because I've since forgotten it and would need to check my notes left it as an exercise for the student. It is a neat little differential equation, and once you work it into the standard form, it's okay not having a closed-form solution, or method of approach, because Bessel functions aren't closed-form. Just look up the function and rescale it by the problem constants.
