Bear in mind that before 1837, there was no such thing as a Wesleyan (or Methodist) marriage. The only bodies allowed to conduct marriages before then were the established Church of England, Quakers and Jews, and unless there is evidence of a Jewish or Quaker connection, the normal place to look for a marriage would be the C of E parish registers.
After 1837 there were other possibilities, though in many cases, while non-conformist church and chapel buildings were licensed for marriages, their ministers weren't authorised to register them, so superintendent registrars used to attend to carry out the registration, bringing the registers with them.
These registers, as far as I know, remain in the register offices, and aren't online as part of, for example, Ancestry's collections of West Yorkshire parish and non-conformist registers. Marriages should be included in the GRO and local indexes, and if you're using YorkshireBMD (or one of the other UKBMD sites) you'll see the location given as "Authorised Building".
Once a chapel had its own registers, when these were full they may have been deposited somewhere and thus potentially be available for public inspection. Registers held in register offices are normally not available to view.
Arthur
