This may be a minor point, but (as a Quaker) I did want to point out, people were married under the care of a Monthly Meeting, which is a spiritual covenant between the couple, those who make up the meeting, and God (or the Divine).
They would not have been married at a Monthly Meeting, which seems to imply that a Monthly Meeting is a place.
The place of the marriage would be where folks gathered to worship, usually the meetinghouse, but it could be elsewhere. The meetinghouse itself is not the Monthly Meeting.
A question might be, in which meetinghouse did the wedding take place in, to find the records. None of the meetinghouses (as far as I can find) were called Philadelphia Monthly Meeting.
The only one with "Philadelphia" in the title that I have seen is Philadelphia Yearly Meeting, which connects several Monthly Meetings in the same area. Wherever they archive the minutes might reveal the marriage, but they would be sorted by meetinghouse.
(Note that for some time around 1828, there were two groups claiming to be Philadelphia Yearly Meeting as there had been a split between Orthodox and Hicksite Quakers. I think best to go with current PYM, which is Hicksite).
Race Street Meetinghouse (now Central Philadelphia Monthly Meeting) was built in 1856, and is on 1515 Cherry St (I don't know why it was named Race St. Mh!) It is still there and in use for many Quaker organizations as well as worship & marriages. There is also an Arch St Friends Meetinghouse in Philadelphia, built in the early 1800's and still there and in use.
There are probably other, smaller Monthly Meetings (and meetinghouses) in Philadelphia, any one of which could be used for a Quaker marriage, some Orthodox, some Hicksite. (Frankfort Friends, started late 1700's, Germantown Friends meeting, Twelfth Street Meetinghouse, Green St Meetinghouse, North Meetinghouse,
Apologies if this was no help or added confusion.