Collect data points in a list into weekly groups?

You can GatherBy using DateValue with "Week" ({"Year","Week"} if the input data spans multiple years) as date element as the second argument:

GatherBy[data, DateValue[#[[1]], "Week"] &]

{{{{2002, 7, 30}, 1.20431}, {{2002, 7, 31}, 0.52822}, {{2002, 8, 1}, -1.51937}, {{2002, 8, 2}, -1.2966}},
{{{2002, 8, 5}, -1.97334}, {{2002, 8, 6}, 1.07311}, {{2002, 8, 7}, 0.224605}, {{2002, 8, 8}, 1.78266}, {{2002, 8, 9}, 0.90241}},
{{{2002, 8, 12}, 0.502187}}}

Additionally, CurrentDate and PreviousDate work too. CurrentDate appears to be implemented in terms of PreviousDate. Of course, NextDate would also work.

GatherBy[data, CurrentDate[First[#], "Week"] &]

{{{{2002, 7, 30}, 1.20431}, {{2002, 7, 31}, 0.52822}, {{2002, 8, 1}, -1.51937}, {{2002, 8, 2}, -1.2966}}, {{{2002, 8, 5}, -1.97334}, {{2002, 8, 6}, 1.07311}, {{2002, 8, 7}, 0.224605}, {{2002, 8, 8}, 1.78266}, {{2002, 8, 9}, 0.90241}}, {{{2002, 8, 12}, 0.502187}}}

GatherBy[data, PreviousDate[First[#], "Week"] &]