Your unit of force will be your basic mass unit times your basic acceleration unit (remember F=m.a?), or in your case:
Force unit = (1/1000) kg . (1/1000)m/s^2=1.0E-6 N
So, your basic unit of force is 1.0E-6 N. (One microNewton).
If you assume g=10 m/s/s (most people use 9.807 or thereabouts - depends on your loaction on the earth), the mass that would have a weight equal to one force unit is 1.0E-6/10 = 1.0E-7 kg. (Don't interchange mass with force or weight - they are not the same thing. A kilogram.force IS a valid force unit, equal to the weight of a 1 kilogram mass subject to 1 g acceleartion - but it is NOT the same thing as a kilogram!)
Your basic stress unit will be one force unit divided by (one length unit squared) = 1.0E-6/(1/1000)^2 N/m2 = 1.0 Pa. Thus, your stress of 2E6 is in fact 2 MPa or 2 N/mm2.
(I hope I have not been too pedantic, but I have found many students have trouble with units, and the best solution is to step through the calculations slowly and steadily.)