com.apple.BKAgentService running at >100% CPU

MacBook Air, mid 2012, 2 GHz Intel Core i7, 8 GB 1600 MHz DDR3, OS X 10.11.6

Since a couple of weeks ago I experience the following strange behaviour:

Upon signing out of one user account, com.apple.BKAgentService starts running from that account at more than 100% CPU and the fans get noisy. In some cases, it stops after a couple of minutes by itself, but mostly I have to kill the process. Strangely enough, I can also stop it by signing in again with that account. As soon as I sign out, however, com.apple.BKAgentService starts running again. I first thought that it only happens with one of my two accounts, but it actually happens with both.

This is what the console says:

can't get sender: Error Domain=NSCocoaErrorDomain Code=4099 "The connection to service named com.apple.bird was invalidated." UserInfo={NSDebugDescription=The connection to service named com.apple.bird was invalidated.}

As far as I can tell after doing some research, this seems to have something to do with iBooks syncing. So I already emptied my iBooks library, signed in and out of iCloud, and deleted the com.apple.bird cache. No luck. In a fit of superstition I also did a NVRAM and SMC reset and even reinstalled El Capitan. Still no luck. Sooner or later com.apple.BKAgentService starts acting weird again.

I'm thankful for any ideas on how to proceed.