@claudiom Perhaps the sites you have pinned are hoggy with RAM and CPU?
Some sites love to continually poll in the background and keep loading lots and lots of data and/or burn the CPU to do various tasks. (Some sites are even mining Bitcoin and other crypto currencies now!)
It's probably worth profiling the sites with devtools in Firefox and/or Chrome.
Keeping the network tab on either's devtools might be enough to show background network rewuests, which would indicate background activity.