The rationale is very loosely based upon the energy required to move you and the proportion of the aircraft that is carrying you.
Taking British Airways as an example, in J the seat pitch x width is 73" x 20" = 1460 square inches. In Y it is 31 x 17.5 = 542.5 square inches. Quite simply, it requires more energy (and thus more emissions) to move the floor area of the J class passenger than the Y class passenger. Or, put it another way, if all the J class passengers sat in economy seats then a smaller aircraft could be used to transport the same number of people, thus reducing emissions.
In reality given the disparity between J and Y class floor areas, the J class passenger should be paying more in relation to the Y class. This is of course even worse when F is taken into account (1683 sq inches). The innovation of flat bed seats in J and F has driven up this differential in recent years.
That is of course the rational argument, although it is also arguable whether a simple floor area claculation is appropriate - more complex formulae could be used easily. The more cynical view might be that J class passengers (or actually in general their employers) have deeper pockets...