Closure systems, kits and methods for sealing a percutaneous puncture or other opening in a blood vessel wall, body cavity or biopsy tract are disclosed. A closure system can comprise an implant assembly, a delivery assembly, and an introducer sheath. The closure system can further comprise a valve bypass and a dilator. The implant assembly can include an inner member, a sealing membrane, and an outer member, each of which can be delivered by the delivery assembly. The inner member can be extended through the puncture or opening and positioned adjacent an inner tissue surface. The outer member can be positioned adjacent an outer tissue surface. The sealing membrane can have a distal end attached to the inner member, a proximal end including an opening configured to receive the outer member, and a mid-region therebetween. The outer member, when expanded from a delivery configuration to a sealing configuration, can urge the mid-region of the sealing membrane radially outward such that its outer surface can contact and conform to a perimeter edge of the puncture or opening.