The OED notes "Now usually considered less formal than quickly, and found chiefly in informal or colloquial contexts." The now at the beginning of that sentence is of interest. The entry has quotations for quick as an adverb from 1300 until the present day with everything in between, and with both formal and informal examples.
In other words, this is not a change, but a continuation, though perhaps we are currently on the ebb of an -ly-ful wave. The Corpus of Current American English shows a slight decline in -ly adverb frequency from 1990-2008 with 11,515 instances per million words in 1990-1994, 11, 291 in '95-'99, 11,146 in 200-2004, and 11,074 in 2005-2008 where, over the same period, all adverbs actually increased in frequency from 35,072 PMW to 35,373.
The Time Corpus shows the same overall increase in adverb use, but for -ly adverbs, it shows a gradual increase from the 1920s with a peak in the 1970s followed by a drop off, today's levels being about the same as they were a century ago.
Also, check out Jan Freeman's "The Word" column from Sept 17, 2006.