The widely used empirical regularity is the square-root law: impact scales roughly with sqrt(order size / daily volume). Doubling an order raises impact by about 40%, not 100%.
Temporary versus permanent is the distinction that matters. Temporary impact is the cost of demanding immediacy and reverts as the book refills - it can be reduced by trading slower. Permanent impact is the market updating on the information your trade revealed, and it does not revert.
The execution trade-off: trade fast and pay impact, trade slowly and take timing risk.