A flexible film package for storing food products comprises a body with a side wall, a closed bottom end, and a closed top end. The body includes a primary line of weakness and a pair of secondary lines of weakness formed in the side wall. Each of the primary and secondary lines of weakness includes a plurality of score lines spaced apart by non-scored portions of the side wall. The score lines of the primary line of weakness have a greater length, width, and depth than the score lines of the secondary lines of weakness. The non-scored portions between the score lines of the primary line of weakness are longer than the non-scored portions between the score lines of the secondary lines of weakness.