The degree is important - it will satisfy the legal requirements and get you a visa and work permit. It is also pretty much required by most of the better employers. The main kind of TESOL certification by the schools that insist on it (most do), is a minimum of 120 hours on a face-to-face course with at least 6 hours of observed teaching.
Some online courses that involve at least 120 hours of study will be accepted, but without the practical element many employers will expect previous teaching experience of some kind, and proof of it.
I my opinion, I don't think there can be adequate training in a course that lasts only a weekend. Such a course is possibly useful as a 'taster', and may be helpful for anyone still undecided as to whether they should embark on a TESOL career or not. One weekend is not even enough time to read through a door-stopper training manual by jeremy Harmer or Penny Ur.