wd = WeatherData["SanDiego", "Temperature", {"Jan. 1, 2014", "Aug. 1, 2014", "Day"}];
wednesdays = Pick[wd, DayName /@ wd[[All, 1]], Wednesday];
sundays = Pick[wd[[All, 1]], DayName /@ wd[[All, 1]], Sunday];
ticks = MapIndexed[{#, Rotate["Week " <> ToString[First@#2], Pi/2]} &,
wednesdays[[All, 1]]];
DateListPlot[wd, FrameTicks -> {ticks, Automatic, None, None},
GridLines -> {sundays, None}, ImageSize -> 600, Joined -> True,
Epilog -> {Red, PointSize[Medium], Point[wednesdays]}]
