Can I fight an eviction appeal as landlord

Yes you can. Once the eviction is appealed after the Justice Court, the new court will hear it "de novo" which means the new court will not look at the arguments made at the Justice Court and all of the facts/law must be re-argued from scratch. Therefore, it's important you attend the new trial and argue it just as well (or better!) than you did at the Justice Court. Do note that technically different rules of civil procedure apply to Justice Court and District/County Courts.