This weaving machine (2) is for simultaneously weaving top and bottom pile fabrics (F2, F4) presenting some pile patterns (P2, P2′, P4) and including tufts, made from warp yarns (24), binding warp yarns (14, 16) and inwoven weft yarns. This machine includes a pile warp yarns feeding unit (20), a binding warp yarns feeding unit (18), a shedding unit (6) and a weft insertion unit (8) for inserting the weft yarns in the shed. The machine also includes a beating-up mechanism (32), a take up system (70), a drawing-in unit (26), and a control unit (80). A treatment unit (90) is located, along a path of the pile warp yarns (24), between the pile warp yarns feeding unit (20) and the shedding unit (6), for applying different segments of treatment on at least some of the pile warp yarns (24).