How to calculate the kinetic order of an enzymatic reaction?
The legal limit in some states of 0.08% BAC corresponds to about 17 mM ethanol in the blood. The $K_M$ value for human liver alcohol dehydrogenase is 0.5 mM according to this paper. So at this particular legal limit, the enzyme works at 97% of its maximal capacity. ($v = v_{max} \frac{[S]}{[S] + K_M}$).

Above or very much above the legal limit, the rate does not change much, making it approximately zero order in ethanol. Because the breakdown of alcohol does not get faster with more intake, it can take past the next morning to metabolize sufficient alcohol to reach values below the legal limit if someone drinks heavily at night.

For ethanol concentrations below the $K_M$, the reaction is approximately first order in ethanol, so it gets slower and slower as the ethanol concentration approaches very small concentration.

While the $K_M$ is the same for different individuals, the amount of enzyme is not (depends on the size and health of the liver, gender, and on genetics). That's where the body mass comes in.