Imperial measurements that are not integers are displayed in fractions.

Often, they're not: look at packaging labels especially in grocery stores. Engineers use decimals regardless of unit.

Weight scales in the US don't mark 1⁄3.

Quarter & third likely show up for verbal ease/brevity of naming: saying 250 grams is a bit of mouthful & unlikely for naming anything. I suspect if Americans used metric, they might still use fractions to refer to burgers by weight/mass in kg (like drugs!).

In metrics, fractions are rarely used.

Also convention. Nothing prevents 1⁄3 kg, 1⁄4 kg, and I'd expect to see 1⁄3 kg more often than 0.3̅ kg if rounding were avoided.

In metric, Americans still would get this wrong, because they don't understand fractions despite using them. Or are you suggesting everyone would get the order of 1⁄3 kg & 1⁄4 kg wrong?