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May be a form of ...
Whatley
English: habitational name from any of various places named with Old English hw?te ‘wheat’ + leah ‘(woodland) clearing’, as for example Whatley in Somerset, Whately in Warwickshire, or any of the places mentioned at Wheatley.
Dictionary of American Family Names,

Or perhaps a combination of:

Waite
English: occupational name for a watchman, Anglo-Norman French waite (of Germanic origin; compare Wachter), or from the same word in its original abstract/collective sense, ‘the watch’. There may also have been some late confusion with White.

Plus -ley which would signify a field or meadow ...thus someone who watched over the fields ...just guesses ...

I did find it in my Irish names book.

Whateley: rare in Ireland, found in Louth-Meath area. It is of English origin from Wiltshire.