For the current release you can use the registry key: HKEY_LOCAL_MACHINE\SOFTWARE\VeeaM\EnterpriseManager\CollectorsObjectCount
on the machine where the nworks Enterprise Manager service is running.
The "data" field, decimal, shows you the actual number of monitored objects per each collector.
Next release this information will be also available in the UI.
Hope, this helps,
P.S. 7K objects is a big overload! We kindly suggest you to install additional collector.