As the two other answers said, more copper equals lower resistance and lower inductance, which measures for high \$\frac{\mathrm{d}\,I}{\mathrm{d}t}\$ things like switching currents through an inductor in a buck converter.
Don't overdo it, though: While not using the thin signal traces you'd use for low currents elsewhere on the board definitely is a good idea, at some point most current will already run on the edges of your trace, and adding more volume just won't help as much. Going wild on PCB copper area won't help immensely much if the bulk of your parasitic effects come from something else!
And: it's probably more important that you improve grounding of U3 than it is to maximize trace width everywhere. Would I review your circuit, I would indeed say "use wider traces", but I'd be more concerned with you trying to carry all U3's ground current through the small via that you use for your feedback voltage divider. That seems like a bad idea; the datasheet's design advice especially tells you to keep the ground path short, between decoupling caps and GND path. You kind of did the opposite: you placed the ground via of the decoupling capacitor as far away from your chip's ground pad as possible without explicitly adding a long trace, and you also routed your device ground on the top layer for a while, further away from both the ground pin and the desirable location of the decoupling capacitor. Simply use two separate vias for your U3 ground pin and the ground of your voltage divider, and flip your C5 around, so that its ground via is closer to the chip.