Running and monitoring and ESXi server, after a short amount of time, the sqlservr program grows to almost hit 1 Gb or RAM. This doesn't seem or should be normal. Any suggestions?
This is really not related to Veeam Monitor, rather to Microsoft SQL design. When actively working, and in case when computer has sufficient memory available, Microsoft SQL reserves some of the memory to work faster.
You can always reduce the maximum size of reserved memory by going into Management Studio, right-clicking the database, selecting Properties, Memory tab. Although there is little sense to do it, best is to leave the default settings for performance reasons.