Losing weight won't lengthen your bones, but it can measurably improve posture, decompress spinal discs, correct postural deformities, and change how tall you appear and carry yourself. This article examines the actual mechanisms.
Bone length is genetically fixed after growth plate closure. Weight loss does not increase height. However, spinal disc compression under body weight, postural changes from abdominal fat, and diurnal height variation (up to 2 cm) are measurable phenomena. This article explains what actually happens to apparent height with weight changes.