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#11
I force installed Update for Windows 7 for x64-based Systems (KB3006137)\WindowsUpdateAgent-7.6-x64.exe (Windows Update Merged Standalone Setup) and ran a few fixes including resetting BITS. After the fixes WU behaves itself and also has updated to 7.6.7601.18937. The following update then installed on July 21 (2015)
Windows Update Client for Windows 7 and Windows Server 2008 R2: August 2015
I haven't had any WU problems for over one month.
RAM usage during Windows Update checks has never been above 175Mb
Previously it was running at anywhere between 1 - 2 GB for hours at a time several times per day.