I'm using SSRS 2008 to create a report, the tablix border looks fine when the zoom level is 100%:
But when I zoom in then the inner border becomes thicker:
How do I avoid this?
"Zoom" uses a scaling effect to scale everything to a different size. Everything is scaled, so that formatting is maintained - you don't get to pick and choose what scales, otherwise your reports formatting would quickly crumble - remember that SSRS formatting is relational, not absolute.
If you want your report to have large text with tiny borders, you need to design it that way - Zoom is not the feature you want.