A Premier account isn't allocated more system resources; it's a way to get technical support from Google. A regular paid account can buy you all the compute power you need.
More likely, the problem is that you're throwing too much data at AppInventor. AppInventor is intended to help get you started on a simple application, not handle huge workloads. You may need to rearchitect your application to use a different storage mechanism. How many saved values are you throwing at the DB, and when you say "collapsed" can you explain further what you mean by that? Are you receiving errors or unusual slowness?