KöMaL 2005 B3834

What is the largest value of the whole number $n$, such that with the help of two appropriately chosen weights and an equal-arm balance it is possible to determine the mass of every object that weighs a whole number of kilograms from 1 to $n$? (It is allowed to carry out as many measurements as needed, only using the two weights and the object to be weighed, and neither the weights nor the objects to be weighted are allowed to be cut in parts.)