Wordorigins.org

Dope has a variety of meanings, most relating to thick, viscous liquids. It is an Americanism, coming from the Dutch doop, meaning sauce.

It first appears in the writings of Washington Irving from 1807, in a sense meaning sauce or gravy:

Philo Dripping-pan was remarkable for his...love of what the Dutch call doup.

This sense expands in subsequent decades to encompass a number of thick, syrupy liquids used for a variety of purposes.