pad (n.) Look up pad at Dictionary.com
1550s, "bundle of straw to lie on," possibly from or related to Low German or obsolete Flemish pad "sole of the foot," which is perhaps from PIE *pent- "to tread, go" (see find (v.)), but see path (n.). Meaning "cushion-like part of an animal foot" is from 1790 in English. Generalized sense of "something soft" is from c.1700; the sense of "a number of sheets fastened together" (in writing pad, drawing pad, etc.) is from 1865.

Sense of "takeoff or landing place for a helicopter" is from 1960. The word persisted in underworld slang from early 18c. in the sense "sleeping place," and was popularized again c.1959, originally in beatnik speech (later hippie slang) in its original English sense of "place to sleep temporarily."
pad (v.2) Look up pad at Dictionary.com
"to stuff, increase the amount of," 1827, from pad (n.); transferred to expense accounts, etc. from 1913. Related: Padded; padding. Notion of a padded cell in an asylum or prison is from 1862 (padded room).
pad (v.1) Look up pad at Dictionary.com
"to walk," 1550s, probably from Middle Dutch paden "walk along a path, make a path," from pad, pat "path." Originally criminals' slang, perhaps of imitative origin (sound of feet trudging on a dirt road). Related: Padded; padding.