The invention discloses a method of and apparatus for forming a bag assembly by RF welding. A single source of RF energy is used to generate a high frequency electric field having a first strength between tube-welding electrodes of opposing die members and a second strength less than the first strength between perimeter-welding electrodes of the opposing die members. Respective portions of the bag assembly are subjected to this variable-strength field simultaneously so that the bag assembly is formed in one welding operation. Stand-offs are used in some embodiments to limit penetration of the electrodes into the weld areas.