As Frank says, the cut function is beginning on Monday, not Saturday. You can change this by using the start.on.monday option to cut
.
> weeklyList <- split(dataSet, cut(dateRange, "weeks", ordered_result = TRUE, start.on.monday = FALSE))
> weeklyList
$`2011-07-03`
[1] 0.8208915 0.3073812 0.7427008 0.6856026 0.7733733 0.6258881 0.5222145
$`2011-07-10`
[1] 0.10739317 0.43350298 0.17186167 0.90407228 0.95883564 0.60972446 0.08929786
$`2011-07-17`
[1] 0.61130816 0.06738358 0.71603027 0.51067438 0.32632549 0.52515075 0.92037779
$`2011-07-24`
[1] 0.1391482 0.4253714 0.2754398 0.5745825 0.8776789 0.2088506 0.9773318
$`2011-07-31`
[1] 0.58218481 0.05610510 0.05400599 0.75924478 0.98367785 0.42556051 0.77251544
$`2011-08-07`
[1] 0.5907571