This is a Scots urban word that means to be pale and and colourless in appearance or off-colour and ill-looking. Note that the second half rhymes with sally, not holly. It can refer to the national skin colour of Scots:
With his peely-wally complexion, freckles and shock of ginger hair, Greg Rutherford looks like he could be Scottish.
The Herald (Glasgow), 30 Jul. 2014.
We know it starts life around the early years of the nineteenth century as the single word peelie for a person who is thin, gaunt or pale. Dictionaries usually suggest it’s an imitation of a slight, high-pitched sound, perhaps a noise that someone in distress might make. If so, it’s linked to another imitative Scots word, peek, for the feeble cry of a small bird or animal, a whine or whimper of complaint, or an insignificant person with a piping voice.
Wherever it came from, peelie became duplicated during the nineteenth century to make peely-wally. Some reference works say that the second half is a nonsense word, but others point to the Scots wally. This isn’t the relatively recent English slang term for a silly or inept person (which is pronounced differently), but means something that’s made of china (a wally dug is a china dog). It’s from an Old English verb meaning to fade. So somebody wally-like was as pale as china. Chambers Dictionary suggests the paleness might be that of old-fashioned dentures, which were once made of porcelain and were commonly called wallies.