Tex. R. Civ. P. 139
When a case is appealed, if the judgment of the higher court be against the appellant, but for less amount than the original judgment, such party shall recover the costs of the higher court but shall be adjudged to pay the costs of the court below; if the judgment be against him for the same or a greater amount than in the court below, the adverse party shall recover the costs of both courts. If the judgment of the court above be in favor of the party appealing and for more than the original judgment, such party shall recover the costs of both courts; if the judgment be in his favor, but for the same or a less amount than in the court below, he shall recover the costs of the court below, and pay the costs of the court above.
Tex. R. Civ. P. 139