A weighing and feeding system for accurate weighing of small quantities of material in pelletized form and feeding the weighed material to processing machines, the system comprising: a) a housing: b) a hopper adapted to contain the material in pelletized form or a Vacuum loader adapted to dispense the material in pellet form; c) a plate the top of which is divided into a rear and a forward section; d) a vibration unit located under the plate; e) a load cell; f) a weighing platform attached to the top of the load cell and located under the vibration unit; g) brackets connected to the weighing platform configured to support the hopper over the rear section of the plate; and h) a controller configured to control the feed rate of material from the system to a process machine; wherein i) the housing encloses the hopper, the plate, the vibration unit, the weighing platform, the brackets, and the load cell; ii) the top of the plate comprises: a tray configured to receive pellets of the material that fall out of the hopper or pellets of the material that are dispensed by the Vacuum loader, the tray being created on the rear section of the plate; and a beginning section of an outlet channel created on the forward section of the plate; iii) an extension of the outlet channel created on an extension of the forward section of the plate, the extension of the outlet channel configured to lead pellets of the material that fall out of the hopper or pellets of the material that are dispensed by the Vacuum loader from the beginning section of the outlet channel to a process machine; iv) the vibration unit is configured to cause pellets of the material to move out of the tray through a small opening at the bottom of a front wall of the tray into the beginning section of the outlet channel and from there in essentially single file through the extension of the outlet channel to the process machine; v) the load cell is configured to determine weights of all of: the plate, the tray and its contents, the outlet channel and its contents, the vibration unit, the brackets, the weighing platform, and, when the system comprises the hopper, the hopper and its contents; and vi) the controller is configured to control the feed rate of material from the system to the process machine by causing the vibration unit to vibrate at a constant frequency while controlling the values of the amplitude and duration of the vibrations provided by vibration unit and based on the weights determined by the load cell in order to synchronize the rate and timing of feeding of material with the operation of the process machine. a) a housing: b) a hopper adapted to contain the material in pelletized form or a Vacuum loader adapted to dispense the material in pellet form; c) a plate the top of which is divided into a rear and a forward section; d) a vibration unit located under the plate; e) a load cell; f) a weighing platform attached to the top of the load cell and located under the vibration unit; g) brackets connected to the weighing platform configured to support the hopper over the rear section of the plate; and h) a controller configured to control the feed rate of material from the system to a process machine; i) the housing encloses the hopper, the plate, the vibration unit, the weighing platform, the brackets, and the load cell; ii) the top of the plate comprises: a tray configured to receive pellets of the material that fall out of the hopper or pellets of the material that are dispensed by the Vacuum loader, the tray being created on the rear section of the plate; and a beginning section of an outlet channel created on the forward section of the plate; iii) an extension of the outlet channel created on an extension of the forward section of the plate, the extension of the outlet channel configured to lead pellets of the material that fall out of the hopper or pellets of the material that are dispensed by the Vacuum loader from the beginning section of the outlet channel to a process machine; iv) the vibration unit is configured to cause pellets of the material to move out of the tray through a small opening at the bottom of a front wall of the tray into the beginning section of the outlet channel and from there in essentially single file through the extension of the outlet channel to the process machine; v) the load cell is configured to determine weights of all of: the plate, the tray and its contents, the outlet channel and its contents, the vibration unit, the brackets, the weighing platform, and, when the system comprises the hopper, the hopper and its contents; and vi) the controller is configured to control the feed rate of material from the system to the process machine by causing the vibration unit to vibrate at a constant frequency while controlling the values of the amplitude and duration of the vibrations provided by vibration unit and based on the weights determined by the load cell in order to synchronize the rate and timing of feeding of material with the operation of the process machine.