Weekend working and the whole rostering/bidding system is a very controversial issue at the moment.
Whilst you may get best guesses from some on whereabouts on a seniority list you need to be to get a chance of getting a certain number of weekends off e.g. - "A3XX, 25% from the top, get every other W/E off" I'm not sure anyone can give you a definitive timescales in terms of “X months" or “Y years" simply because your rate of movement up a list depends on all sorts of unknowns.
Just for the sake of overview I'll offer that there are lots of grumbles from the Junior and not so junior on both Longhaul and Shorthaul that getting weekends off under JSS is difficult, and guaranteeing specific weekends free is problematic for almost everybody, regardless of seniority, unless they resort to using Golden days ( 6 per year) qnd/or leave or Duty Free Weeks.