1
general::
Taking into consideration, because of, as in What with all you have to carry, we should take a taxi. This usage replaced the earlier what for. [c. 1600]
American Heritage Idioms
2
general::
Phrase(s): what with something
because of something. • What with the children being at home and my parents coming to stay, I have too much to do. • The Smiths find it difficult to manage financially, what with Mr. Smith losing his job and Mrs. Smith being too ill to work.
McGrawhill's American Idioms And Phrasal Verbs