The present invention relates to an innovative method for estimating the value of the weight of the contents of the oscillating assembly of an electronically controlled household appliance, wherein the oscillating assembly is connected to the frame by means of a suspension system comprising at least one damper (1). The damper (1) comprises at least two elements adapted to move reciprocally, at least one magnetic element, preferably at least one permanent magnet (9), and at least one magnetic sensor, preferably a Hall effect or magnetoresistive sensor (12). The magnetic element and the magnetic sensor are housed in the damper (1) so as to detect the reciprocal motion of the two elements, and the magnetic sensor can generate an electric signal depending on the distance between the two elements. The method comprises the steps of: i) reading an initial value of an electric parameter, in particular voltage, of the electric signal when the oscillating assembly of the household appliance is empty; ii) identifying a mathematical function on the basis of the initial value and of a plurality of predetermined parameters, which relates the electric parameter, in particular voltage, to the weight of the contents of the oscillating assembly of the household appliance; iii) reading a further value of the electric parameter, in particular voltage, after said contents has been loaded into the oscillating assembly, and iv) estimating the value of the weight of said contents by using said mathematical function and said further value of the electric parameter. The present invention also relates to a household appliance adapted to implement said innovative method.