I don't know why will you want 10K variation. do you want to replace 10K with some form of logic?

According to my knowledge, Resistance and Current? it is easier to work on the voltage :)

I know of this following configuration that is used for 12-bit Binary Weighted Resistance. I don't know if it might be of a help to you. Start with the following:
MSB = 1M, then keep on halving it till 0.48K one side will be switched by the uC, and you connect the other sides of the resistors together to the -ve input of the op-amp together with the feedback resistor. and the rest is the calculations.

IF you would like to do a BCD Weighted,
Let the MSB of first digit be
1) 10M ohms, then halve it
2) 5M ohms
3) 2.5M ohms
4) 1.25M ohms

then for Second digit let the MSB be
1) 1M
2) 500K
3) 250K
4) 1.25

then for last digit
1) 100K
2) 50K
3) 25K
4) 12.5K