Generally yes, using 1oz or 2oz copper does help add thermal mass and reduces ground system sheet resistance.
One thing to be aware of when using thicker copper foil is that it affects fine-pitch traces - normally we assume the vertical shape of the etched traces is ideal, since the traces are more wide than thick. But very thin traces etched in relatively thick 2oz foil, start to have noticeable trapezoidal walls due to non-ideality of the etch process. PCB vendors generally know how to compensate to some extent, but if there are any 0402 or smaller components on the board, I'd stick with 0.5oz copper for the outer layer. In your example I don't see anything that looks like it would be a problem.
Side note about the inductor heating: check the datasheet for the inductor, there are two ways that the max current is rated. There is a magnetic saturation limit where the effective inductance is reduced by 10%, and there is a temperature limit where the component temperature reaches some threshold. Some vendors (like TDK or Sumida) give both limits separately, other vendors might list only one of these. Either way, if the inductor is getting that hot, it's likely undersized for the peak current. There is a practical limit to how much energy an inductor can store, ½LI². For your Vishay inductors, the Heat Rating test condition is based on a temperature rise of 40°C above ambient, so 70°C sounds like it is at or near heat saturation.