when travelling within the usa do airlines check for misdemeanor warrants?

Airlines don't check for warrants, they only check names against the No Fly list.

NO, they have no access to the system. Most airports do have police that can, but if you stay out of trouble you wont have to worry about this. There is an easy way to not have to worry about this, tale care of the warrant.

If traveling within the U.S. no. If you travel to Mexico or Canada, or for that matter overseas then you are checked, but not by the airlines. Thinking that you might be skipping the country.