Metric, definitely.
(unfortunately, most of our playerbase is probably american, but we're devs, har-har.)
This could be coded into the loadout, and is certainly possible.
(see : bay, with you being able to choose your body type such as height and weight and you can see it when you examine them , e.g : Greytide McBaldie is of normal height and slightly overweight.)
And the measuring tape could just spit out the actual number. Here's how it would go.
If you put your height to be...
80 units to 130 units, you would be examined as short.
130 units to 180, examined as average.
180 and above, examined as tall.
But if you want the EXACT number in the character loadout, you need the measuring tape.
Same could be applied for weight.