It really varies from school to school and district to district. Some districts and schools move on to the next tier after 2 weeks, others 6 months. I tend to carry out interventions on the longer side, especially with tier 2 and 3. I don't think I would ever recommend moving on after 2 weeks. That doesn't seem nearly long enough to shape a student's behaviors and patterns.

I usually ask the most resistant teachers to give each tier AT LEAST 6 weeks, but this is really a bare minimum and starting point in my mind.

This will also depend somewhat on the individual student as you get into tier 2 and 3.