kind of casual shoe, 1937, from topside in nautical sense of "upper deck of a ship," where the rubber soles would provide good grip; from top (n.1) + side (n.).
Entries linking to top-sider
top n.1
"highest point," Old English top "summit, crest, tuft," from Proto-Germanic *toppa- (source also of Old Norse toppr "tuft of hair," Old Frisian top "tuft," Old Dutch topp, Dutch top, Old High German zopf "end, tip, tuft of hair," German Zopf "tuft of hair"); no certain connections outside Germanic except a few Romanic words probably borrowed from Germanic.
Few Indo-European languages have a word so generic, which can be used of the upper part or surface of just about anything. More typical is German, which has Spitze for sharp peaks (mountains), oberfläche for the upper surface of flat things (such as a table). The meaning "highest position" is from 1620s; the meaning "best part" is from 1660s. The sense of "dominant sexual partner" is by 1961.
To go over the top is World War I slang for "start an attack," in reference to the top of the trenches; as "beyond reasonable limits, too far" it is recorded from 1968. Top of the world as "position of greatest eminence" is from 1670s. Top-of-the-line (adj.) is by 1950.
side n.
Old English side "flanks of a person, the long part or aspect of anything," from Proto-Germanic *sīdō (source also of Old Saxon sida, Old Norse siða, "flank; side (of meat); coast," Danish side, Swedish sida, Middle Dutch side, Dutch zidje, Old High German sita, German Seite), from adjective *sithas "long" (source of Old English sid "long, broad, spacious," Old Norse siðr "long, hanging down"), from PIE root *se- "long; late" (see soiree).
The "long part of anything" sense is preserved hillside, it also was in 16c.-17c. side-coat "long coat." From 14c. as "lateral half of the body of a slaughtered animal." In reference to bacon, it indicates position relative to the ribs. The meaning "a region, district" is from c. 1400, as in South Side, countryside.
The figurative sense of "position or attitude of a person or set of persons in relation to another" (as in choose sides, side of the story) is recorded by mid-13c. As "an aspect" of anything immaterial (the bright side, etc.), by mid-15c.
The meaning "one of the parties in a transaction" is from late 14c.. The sense of "one of the parties in a sporting contest or game" is from 1690s. The meaning "music on one side of a phonograph record" is attested by 1936. As short for side-dish, by 1848.
The phrase side by side "close together and abreast, placed with sides near together" is recorded from c. 1200. Colloquial on the side "in addition," especially "unacknowledged," with connotations of "illicit, shady," is by 1893.