A thing which has grease is greasy. A person who lacks sleep is sleepy. A thing which can cause a slip is slippery. These inconsistencies are inescapable in English, but I think I finally satisfied my curiosity about the extra syllable in “slippery.”

SLIP, to creep or glide along, to slink, move out of place, escape; also, to cause to slide, omit, let loose. (E). We have confused the strong (intransitive) and weak (transitive) forms; or rather, we have preserved only the weak verb, with pt. t. slipped, pp. slipped or slipt. The strong verb would have become *slipe, pt. t. *slope, pp. *slippen, long disused; but Gower has him slipeth (used reflexively), riming with wipeth C. A. ii. 347; bk. v. 6530. Gower also has he slipte (wrongly used intransitively), from the weak verb slippen; ... The AS. adj. sliper, slippery, is from the weak grade of the pp.

--Etymological Dictionary of the English Language, WW Skeat