wd = WeatherData["SanDiego", "Temperature", {"Jan. 1, 2014", "Aug. 1, 2014", "Day"}];

    (*   for version 10+ evaluate:  wd = wd // Normal // QuantityMagnitude;   *)

    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, BaseStyle -> Thick, AspectRatio -> 1/4, 
     FrameTicks -> {ticks, Automatic, None, None}, 
     GridLines -> {sundays, None}, ImageSize -> 900, Joined -> True, 
     Epilog -> {Red, PointSize[Medium], Point[wednesdays]}]
![enter image description here][1]


  [1]: https://i.sstatic.net/KggvY.png