A coated textile sleeve for routing and protecting elongate members, combination thereof, and method of construction is provided. The textile sleeve has an elongate knit wall constructed from weft knit yarns. The knit wall has an inner surface providing a generally tubular cavity in which the elongate members are received and protected. The inner surface is formed, at least in part, by laid-in yarn to provide a soft, non-abrasive surface for dampening contact with the elongate members being protected to facilitate absorbing vibration, which in turn, reduces the frictional wear of the elongate members being protected. Further, the knit wall has an outer surface with a flexible, impervious elastomeric coating thereon. The elastomeric coating allows the knit wall to substantially retain its flexibility as knit, provides enhanced protection against the ingress of fluid and other contaminants, and providing added dampening to absorb vibration.