total size of group of files selected with 'find'

I'd like to promote jason's comment above to the status of answer, because I believe it's the most mnemonic (though not the most generic, if you really gotta have the file list specified by find):

$ du -hs *.nc
6.1M  foo.nc
280K  foo_region_N2O.nc
8.0K  foo_region_PS.nc
844K  foo_region_xyz.nc
844K  foo_region_z.nc
37M   ETOPO1_Ice_g_gmt4.grd_region_zS.nc
$ du -ch *.nc | tail -n 1
45M total
$ du -cb *.nc | tail -n 1
47033368  total

The command du tells you about disk usage. Example usage for your specific case:

find rapidly_shrinking_drive/ -name "offender1" -mtime -1 -print0 | du --files0-from=- -hc | tail -n1

(Previously I wrote du -hs, but on my machine that appears to disregard find's input and instead summarises the size of the cwd.)

with GNU find,

 find /path -name "offender" -printf "%s\n" | awk '{t+=$1}END{print t}'

Darn, Stephan202 is right. I didn't think about du -s (summarize), so instead I used awk:

find rapidly_shrinking_drive/ -name "offender1" -mtime -1 | du | awk '{total+=$1} END{print total}'

I like the other answer better though, and it's almost certainly more efficient.