You can use volumetric measurement...
It is not further weighing, but it starts with weighing an amount with limited accuracy, and then dissolving that amount in a precise volume of a solvent. Using liquid measurement equipment like cylinders and small needle-less syringes you can use that as a sort of multiplier on your accuracy.
So for example if you weigh a gram, more or less, then you can dissolve that in water or alcohol, say 10 ml. If you have precise syringes you can then measure whatever fraction you want, IF you have markings on your 'barrels' that allow gauging such exact volumes.
Mind you, you can weigh liquids and using their densities convert the volume into weight, though again - quite an error margin. Better is to use like a kitchen pitcher with volume markings. Oral syringes can be bought at pet stores for giving medicine.
There is a centralized volumetric measurement thread in the PD forum (follow the Psychedelic Index and find those keywords)...
Beyond that, there are very sketchy ways to make mechanical balances that give you accuracy but that is not what you want... So there are not good alternatives besides getting a milligram scale (they are cheap, again centralized thread on it in PD)