Alix Earle has a heavyweight in her corner amid her feud with Alex Cooper ... 'cause Carl’s Jr. is standing firmly behind its Super Bowl star, TMZ has learned. A Carl's Jr. spokesperson tells TMZ ... "While there seems to be plenty of beef circulating online lately, we promise ours is the juiciest. Alix’s authentic style was the perfect fit for our campaign. She is the best in the business at post-game recovery, so it was a natural fit." The star burger company adds to the quippy statement ... "