How do I get transactions with zero balance not to print on the Balance Sheet?

Hello there, @Urkel.

Removing the zero balance in the report is quick and easy. To get started, you can pull up and customize the Balance Sheet report from there, you can Except zero amount. Please see the detailed step below.

1. Go to the Reports from the left menu.
2. Type Balance Sheet in the search bar.
3. Click Customize at the top.
4. Under the Accounting method, tick the box beside the Except zero amount.
5. Hit Run report.

Then, you can have the Balance Sheet report memorized to save its current customization settings. You can refer to this article for the detailed steps: Memorize reports in QuickBooks Online. 

Please know you can continue to reach me here with any additional questions. Thanks for coming to the Community, wishing you continued success.