The artistic use of the "pennyweight" illustrates, now, the age of this song. At the time of its writing, it was common to express something as a pennyweight, because of the old systems of measurement. A pennyweight is a very small weight, and shows that Work was being very minute in his description.
The actual definition, if anyone is interested:
A pennyweight (abbreviated dwt) is a unit of mass that is equal to 24 grains, 1⁄20 of a troy ounce, 1⁄240 of a troy pound, approximately 0.054857 avoirdupois ounce and exactly 1.55517384 grams. In the Middle Ages, a British penny's weight was literally, as well as monetarily, 1⁄20 of an ounce and 1⁄240 of a pound of sterling silver. At that time, the pound in use was the Tower pound (5,400 troy grains). The medieval English pennyweight was thus equal to 32 Tower grains (also known as wheat grains). When Troy weights replaced Tower weights in 1527, the Troy weights were defined in such a way that the old Tower pound came out to exactly 5400 Troy grains (also known as barleycorns), the Tower pennyweight 221⁄2 Troy grains (and thus approximately 1.46 grams). After 1527, the English pennyweight was the Troy pennyweight.