Walking
Old English wealcan ‘roll, toss’, also ‘wander’, of Germanic origin. The sense ‘move about’, and specifically ‘go about on foot’, arose in Middle English.
wiktionary
From Middle English walkynge, walkinge, walkinde, walkende, walkand, walkande, from Old English wealcende (attested as Old English wealcendes), from Proto-Germanic *walkandz, present participle of Proto-Germanic *walkaną(“to roll, trample, walk”), equivalent to walk + -ing.
From Middle English walkyng, walkinge, equivalent to walk + -ing.
etymonline
walking (adj.)
c. 1400, present-participle adjective from walk (v.). Walking sickness, one in which the sufferer is able to get about and is not bed-ridden, is from 1846. Walking wounded is recorded from 1917. Walking bass is attested from 1939 in jazz slang. Walking stick is recorded from 1570s; the insect so called from 1760, for resemblance of shape.