Hi Ellie
Someone suggested a marriage in 1961
If you start with that and use
http://freebmd.org.uk then you can find the bride's surname and then search for births after the marriage, surname Weaver and mother's maiden name as shown for the marriage.
I can see three children listed born Durham City but none have the first name that you are looking for. However, the FreeBMD records have not all been transcribed for that period so try searching on
http://www.findmypast.co.uk/ There is a birth in 1963 which might be the one you want, if Durham turns out to be the right area.
Once you find that entry, just google for the first name plus initials and surname and see what comes up.
I don't know if that is the person you are looking for or not, but wish you all the best.
(Trying to keep this as helpful as possible without, I hope, infringing the rules)