How did Fechner justify the assumption that the just-noticeable-difference in sensation is constant?
It was not an assumption; it was a decision. It allowed for better quantification, it gave an operational definition in increase in sensation, which allowed for more common ground in research between different labs. In a way, it's a definition by pure counting: when the subject feels a change in sensation, add one. Then this absolute scale is plotted against the ratio scale of increase in stimulation.