How is Visual Guard .Net supposed to impact my application? Is the runtime integrated to each copy of my application? could this make it bigger? Do I need a more powerful server if I secure a Webform application?

To install Visual Guard .Net on the developer machine, you need about 50 MB.
In the database you need a few Mo when you install VG. The size of the repository will grow depending on the number of end users, of applications, Permissions and Roles you will declare.
It also depends on your auditing strategy (the more events you log, the larger the repository).
For example, you can expect the repository size to increase by 10 to 20 MB if you create 5000 user accounts.
Each application will include a few MBs in deployment for the runtime of Visual Guard, in charge of communicating with the repository.
You do not need a more powerful server for a web application secured with Visual Guard.