There is no limit to the amount of assessment they can actually make against your property if a property improvement district is approved.
From Texas local government code:
Sec. 372.019. SUPPLEMENTAL ASSESSMENTS. After notice and a hearing, the governing body of the municipality or county may make supplemental assessments to correct omissions or mistakes in the assessment relating to the total cost of the improvement.
So if the petition asks for too small an amount they don’t need your permission to spend more money.
We deserve better