This is exactly what you can do with VEEAM. You can even set your backup strategy to continious integration. As soon as one backup up for the virtual machine is done another incremental will be created; with minimal impact on I/O performance. To save backup-disk-space you may want to enable deduplication in VEEAM.

When you browse you backups you can choose from the available backups and you can open and browse the complete file system at this specific date and time. You can restore one or more specific files or directories directly back to the origin destination or copy & paste them to a different location on any target. You also can start the entire VM directly from backup at this state in an isolated environment to access the system as a working machine. There are tons and tons of more features inside this backup solution.

We run this solution in our office and for most of our customers with virtualized environments. There is even a free version of veeam that lacks datacenter features but you can backup your VMs.

Our usual backup intervals between 8a.m. and 9p.m. is 2 hours. We ensure to have about 5 to 8 restore points during work ours.

So you will have to choose the Tuesdays version of the file at a specific time.

You may want to give it a try if you're running ESXi or Hyper-V.