Metering bandwidth on a per-app/process basis, even website-specific

Are there any Debian apps that will track bandwidth consumption on a per-app basis, and ideally website-specific when a browser with sandboxing has multiple tabs?

These tools are vaguely described as being able to monitor network traffic:

iftop, nload, nethogs, vnstat, bmon, iperf, netperf, iptraf, cbm, zabbix, nagios, cacti, darkstat, sarg, monitorx, etherape

I’ve tried iftop, nload, vnstat, & bmon. Some of those are just showing realtime stats (bytes per second) and some are per net interface, not per app. I need to know the total bandwidth used on a per-process basis so if a website is streaming or buffering something heavy like video I can react. Since browsers tend to have sandboxing, i think there is a separate process per website. So if a website is a pig I need stats on it.

Ultimately I’m on a limited connection and it’s a mystery what is hogging my bandwidth allowance. I prefer light non-graphical apps but I guess I can’t be too fussy at this point.