As Honeygain is a completely passive income application, browsing the web or doing other network activities does not influence your earnings whatsoever.
For example, watching streaming services such as Netflix, and YouTube, listening to Spotify, or downloading games on Steam will not increase your Honeygain bandwidth sharing.
This is due to the fact that the earnings you receive depend solely on the demand for traffic in your country as well as the number of simultaneous Honeygain users in your region. The Honeygain application automatically adjusts to these factors.
All in all, web browsing or intensive usage of your network would not influence your earnings, as your browsing of the web has no influence on the demand for traffic in your region for the use cases of Honeygain.
If you wonder how to increase your Honeygain earnings please read here.