In this construction "to" is a preposition. You need the -ing (gerund) form of the verb to use as the object of the preposition, since the infinitive can't serve that function.

Here’s the detailed explanation ☺️

The expression is ‘to be used to something’ Examples: I’m used to the heat. I’m used to breathing. I’m used to breathing and eating. I’m used to breathing and to eating. (It’s not necessary to repeat the ‘to’ and sounds awkward)