I guess you could create an alias for wget
to always log to a global file:
alias wget='wget -a ~/tmp/wget.log '
Then for every downloaded file there should be a log like this:
Length: 82651 (81K) [text/html]
Saving to: ‘index.html’
0K .......... .......... .......... .......... .......... 61% 62.5K 0s
50K .......... .......... .......... 100% 151K=1.0s
Last-modified header missing -- time-stamps turned off.
2013-12-27 10:30:58 (80.4 KB/s) - ‘index.html’ saved [82651/82651]
So you could use your favorite text processing tools to extract the downloaded bytes, for example:
sed -ne 's?.* saved \[\([0-9][0-9]*\)/.*?\1?p' ~/tmp/wget.log
or
awk '/^Length:/ {print $2}' ~/tmp/wget.log