By using Grams rather then liquid measurements you have to keep track of every substance your working with. It sounds unorthodox why would they do this?
Speaking in terms of how this relates to medicine, the recommended dosages of all medications are going to be determined on a case by case basis, meaning the dosage is specifically determined for each medication. Since you're only dealing with one medication at a time, each one has a dosage and an administration protocol associated with it, so it's actually quite straightforward.
Since you're usually dealing with extremely small quantities of a given drug, the metric system is preferable because it allows far greater precision when dealing with these tiny quantities. I'd rather have a medication expressed as ".05mg" than "1/516 oz". Far easier to deal with when dosage changes are called for as well. Frequently it's a merely a matter of moving the decimal and not much more.