Combination of Biologic and Anti-obesity Therapies in Psoriatic Arthritis

This is a trial to find out how weight loss (achieved by the use of tirzepatide) or ixekizumab treatment affects the characteristics of skin, joint and adipose tissues in patients with Psoriatic Arthritis, Psoriasis and obesity/overweight BMI \>=27. Patients will be randomised to three groups- tirzeparatide only, ixekizumab only or both drugs. They will have an ultrasound guided synovial biopsy, a 4mm punch skin biopsy, alea skin tape sampling and a needle aspiration fat biopsy at baseline, and then be followed up for 52 weeks. Disease activity will be monitored throughout the trial (both examination and clinical questionnaires), and participants in the tirzepatide only group not in PsA minimal disease activity (with \> 1 swollen joint, \>1 tender entheseal point or PASI \>1/BSA \>3%) at weeks 12, 24 or 36 will be offered the addition of Ixekizumab. As well as the biopsies, bloods and urine will be taken at weeks 0, 4, 12, 24, and 52; urine samples taken at weeks 0, 12 and 36; and an additional alea skin tape sample at week 4. Participants have the option to have additional synovial, adipose or skin biopsies at 36 weeks. The primary objective will be to evaluate the molecular changes in repeated synovial, skin and adipose biopsies, and alea skin tape sampling associated with weight loss at 12 weeks (with additional analysis at 36 weeks if patients consent for optional biopsy. The secondary objectives will be : * To evaluate the molecular changes in blood samples associated with weight loss at weeks 4, 12, 36 and 52. * To evaluate how the molecular changes associated with weight loss differ and/or complement those associated with immunomodulation in PsA * To evaluate how the molecular changes associated with weight loss (with/without immunomodulation) relate to disease activity measures.