Hi Marp,
I had a look at the church registers for you.
The baptism provides some useful information:
Name: William BURLEY, 1st child, son of
Father's details: Paul BURLEY servant son of the late Richard BURLEY of Green Hammerton tailor by Hannah his wife
Abode: Feasegate
Mother's details: Elizabeth daughter Robert BURN of Beverley gardener
Born: 14 Feb 1805, baptised 21 Feb 1805
So William's mother is Elizabeth BURN.
The two marriage entries are very odd the first on 18 Oct 1804 says Paul BURLEY is of Dringhouses/servant/bach/age 30 and Elizabeth BOND/otp/spinster/age 21 - the marriage was by licence. Witnesses John Tale and Geo. Brown
The second on 10 Jan 1805 says Paul BURLEY is otp/servant/age 30 and Elizabeth BURN otp/age 21 - this time it is by banns. Witnesses Elizabeth Burley and Thomas Rounding. No marital status is given for the couple at the second marriage.
At both ceremonies Paul BURLEY makes his mark and Elizabeth signs.
My gut feeling is that it is the same couple but why two ceremonies and the differing names for Elizabeth I have no idea

I hope this is of some help.
Pinetree