over() in sp package

Hi,

When I call:

over(spPolyDf, spGridDf)

The function seems to be returning the spGridDf$band1 value for the first
grid cell that is contained in each polygon.

What I would like is an overlap-area weighted average (or some provided
function like sum) of all the grid cells contained (or partially contained)
in each polygon element of spPolyDf.

I have code that does this by eventually using joinPolys() from PBSMapping,
but it's slow and would be much cleaner to have a sp-only solution. Is
there any way to do this? Some example code is below:

library(sp)
library(rgdal)

# Download a USA shapefile
tmpFile <- tempfile()
download.file("
http://www2.census.gov/geo/tiger/GENZ2013/cb_2013_us_state_20m.zip",
destfile = tmpFile)
unzipped <- unzip(zipfile = tmpFile, exdir = getwd())

# This is the actual reading stage
states <- readOGR(getwd(), layer="cb_2013_us_state_20m")

# Remove all the files on disk
file.remove(tmpFile)
file.remove(unzipped)

tmpFile <- tempfile()

url <- paste0("http://www.prism.oregonstate.edu/fetchData.php?type",
              "=bil&kind=recent&elem=tmax&range=daily&temporal=",
              "20140416")

# Download the file to fileName
download.file(url = url, mode = "wb", destfile = tmpFile)

# unzip the file to the working directory.
unzippedFiles <- unzip(zipfile = tmpFile, overwrite = TRUE)

# read into R
tMaxGrid <- readGDAL(fname = unzippedFiles[1])

# delete the file
file.remove(tmpFile)
file.remove(unzippedFiles)

# This doesn't work correctly
states$tmax20140416 <- over(states, tMaxGrid)

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