Not just a higher rate, you will have to pay more interest sooner on the new loan.
Look at the amount of principal you are paying per payment now. Then go look at the amortization table for a new loan. The interest is front loaded.
People who refi after spending, lets say, 5 years paying mostly interest generally don't calculate that part in their break even analysis. IMHO you should only refi if you can shrink your term as well as your rate. Go from a 30 year to a 15 year is a really good deal. Look at the amortization table to see it as you are paying so much more principal each payment.
Or, if you really need the cash for emergency or to make an investment that would recover your new interest expenses(relative to being further along on the principal repayment schedule) then of course you do what you have to do. 7 years left on a 30 year loan is mostly principal remaining.
plug in your original loan amount, term, and interest rate into this and see how much interest is left with only 7 years to go:
https://www.creditkarma.com/calculators/amortization/