By default, Breeze writes each check for the full amount of the invoice, but you can easily edit the amount and make a partial payment.
Go to Accounting > Accounts Payable > Make Payments and locate the invoice you are going to pay.
If you click the amount, the field becomes available for editing.
Enter the new amount and Save. Select the payable and click Make Payments, and Breeze will generate a check for the partial amount.
That's all there is to it!