Three new bills up in the Texas legislature this year take aim at a passage in the tax code that counties are saying has sharply increased the number of lawsuits against appraisal districts in the state — and taxpayers are footing a $16.1 million bill to cover the litigation. Sands Stiefer, the chief appraiser for Harris County, said the city is currently dealing with 5,200 appraisal appeals, including 190 office buildings. "We've got 33 of 34 downtown high-rises in litigation for 2013, and all…