Ok I just fired up a traffic monitor application and played around in D3 for a few minutes (hardly scientific but it should give us a rough idea). Smashed up some big mob packs in Act IV, plenty of stuff happening on-screen.

D3 was responsible for 1.3 MB downloaded and 500k uploaded in 6 minutes, suggesting it'd use ~13MB down and ~5MB up per hour.

So yeah, whatever is responsible for OP's issue, it ain't D3.