schlep v.

early 14c., slippen, "to escape, to move softly and quickly," from an unrecorded Old English word or cognate Middle Low German slippen "to glide, slide," from Proto-Germanic *slipan (source also of Old High German slifan, Middle Dutch slippen, German schleifen "to glide, slide"). This is probably from PIE *sleib-"slip, slide," from root *(s)lei- "slimy, sticky, slippery" (see slime (n.)). The verb is not found in Old English, which did have related adjective slipor "slippery, having a smooth surface." Related: Slipped; slipping. 

It is attested from mid-14c. in the sense of "lose one's footing, slide suddenly and unawares," also "slide out of place," also "fall into error or fault." The meaning "pass unguarded or untaken" is from mid-15c. That of "slide, glide, pass smoothly and easily" is from 1520s.

The transitive sense of "cause to move with a sliding motion" is from 1510s; the meaning "insert surreptitiously, put or place secretly" is from 1680s. The meaning "let loose, release from restraint" (1580s), is probably from the noun sense of "leash for a (hunting) dog that can be easily released" (1570s).

To slip on "put on (clothing, etc.) loosely or in haste" is from 1580s; to slip off "take off noiselessly or hastily" is from 1590s. To slip up "make a mistake, err inadvertently" is from 1855; to slip through the net "evade detection" is by 1829 (for slip through the cracks see crack (n.)). To let (something) slip originally (1520s) was a reference to hounds on a leash; figurative use for "allow to escape through carelessness" is by 1540s.

c. 1300, dragge, "dragnet," perhaps from a Scandinavian source (compare Old Norse dragga "a load," Swedish dragg "grapnel") or from Old English dræge "dragnet," related to dragan "to draw" (see drag (v.)).

From 1708 as "anything attached to a moving body that retards its progress." As the name of a device for retarding or stopping the rotation of wheels, 1795. Sense of "annoying, boring person or thing" is 1813, perhaps from the mechanical senses or the notion of something that must be dragged as an impediment.

Sense of "women's clothing worn by a man" is by 1870, perhaps originally theater slang, from the sensation of long skirts trailing on the floor (another guess is Yiddish trogn "to wear," from German tragen); drag queen "male transvestite or cross-dresser" is from 1941.

Drag racing (1947), is said to be from thieves' slang drag "automobile" (1935), perhaps ultimately from slang sense of "wagon, buggy" (1755), because a horse would drag it. By 1851 this was transferred to "street," as in the phrase main drag (which some propose as the source of the racing sense).

In addition to the time trials there are a number of "drag races" between two or more cars. They are run, not for record, but to satisfy the desire of most Americans to see who can get from here to there in the fastest time. [Popular Mechanics, January 1947]