Yes, if you make more money, you pay more in taxes, but only on the extra amount you earn. Overtime doesn't get a special or extra tax; it just adds to your total income. If your overtime pushes you into a higher tax bracket, only the part of your income that goes over that threshold is taxed at the higher rate, not all of it. For example, if the tax bracket jumps from 12% to 22% at $40,525 and you make $40,600 due to overtime, only the $75 over $40,525 is taxed at 22%, not your entire income.
So, you're not paying a separate, higher tax just because you're working overtime—you're just earning more, so you may pay more overall. The government collects more taxes because you’re earning more, but it’s not like they’re adding an extra tax on overtime itself.