My residency is Louisiana but I work in Texas (I have a small weekday apartment) and go home on weekends. Do I still pay LA income tax?

Since your residence is still in Louisiana, you must still pay LA resident income tax.  If you wish to change your residency to Texas, you will need to obtain a Texas driver's license, register your car in Texas,etc. and move to Texas

Louisiana is a domicile state. All individuals who are domiciled, reside, or maintain a permanent place of residence are required to file a Louisiana individual income tax return and pay taxes on applicable income.  

Federal income tax returns with Louisiana addresses are provided to the Louisiana Department of Revenue by the Internal Revenue Service. For income tax purposes, leaving the state temporarily does not automatically constitute a change in the taxpayer’s residency status. In order to express intent to establish a new place of residence outside of Louisiana, the taxpayer must take certain actions. For example, obtaining a drivers’ license, registering to vote, enrolling children in another school, and registering vehicles are all ways an individual can change their residency status.