A packaging web is disclosed. The web is an elongate, flattened plastic tube having face and back sides delineating the faces and backs of a set of side by side bags. The tube includes an elongated top section and spaced sets of side seals each extending transversely from the bottom to a location near the top section. The side seals of each set delineate sides of adjacent bags such that the sides and bottoms delineate the perimeters of a set of open top bags. The top section is essentially a bottom open tube for providing bag support when the web is fed into a bag loading machine. The web includes superposed, spaced lines of weakness in each of the face and back sides delineating tops of the bags. Each such spaced line of weakness extends substantially across an associated bag top and terminates in spaced relationship with an associate one of the spaced lines of weakness to leave solid sections in the face and back sides.