Diode circuit analysis
Forward biased normal PN junction diode would act as a voltage regulator.so the voltage drop across the diode may be even 0.7V. when we decrease the load resistance(connected across the diode) the current drawn by the diode decrease and the voltage drop also reduces(when a lighter load is connected across the diode it would behave like a good regulator even when there are changes in the supply voltage this is known as LINE REGULATION;but when there is a change in the load it would not hold good LOAD REGULATION).

In other words the dynamic forward resistance of the forward biased diode would increase, if there is a reduction in the current flowing through the diode(the current flowing through the diode would reduce, when the load resistance is decreased)