Would I benefit more by carrying my tuition T2202 over to next year when I make more income?

There's a chance your refund was lowered because of the Working Income Tax Benefit (WITB).

When you begin your return, you usually put in your income first. Because most students have fairly low incomes, a credit known as the Working Income Tax Benefit (WITB) is automatically assigned if you meet the requirements. One of the requirements of this credit is that you were not a student during the year. As soon as you enter in tuition amounts, that credit is removed because you no longer qualify, therefore bringing down your refund.

As tempting as it may be to not enter in your T2202A amounts to keep the higher refund, you shouldn’t – for two very important reasons

Compliance with Canada Revenue Agency (CRA). If you were a student, you don’t qualify for the WITB. Claiming the credit if you don’t meet the requirements is considered non-compliance. Not only will CRA discover this when they begin their internal matching process and claw back that credit, but you may also face interest penalties and fines. 
You’d be shorting yourself in the long run. Even if you don’t need those tuition credits this year, they are a big cushion in your favor when your education pays off and you start making higher income.

As see in the Canada Revenue Agency (CRA) link: Carry forward the amount

You can carry forward your current year’s unused federal tuition fees (that you did not transfer) to claim in a future year, and any unused tuition, education, and textbook amounts carried forward from years prior to 2023, that you cannot use this year. You have to claim your carry forward amount in the first year that you have to pay income tax. To calculate the amount you are carrying forward, you have to file an Income Tax and Benefit Return and fill out  federal Schedule 11.

Thank you for choosing TurboTax.