Load cell without In-amp
You will never be able to get accurate amplification of a 1mV full scale DC signal with a simple circuit using discrete components (I do know a way, but it's not simple). Even a crappy LM324 will do better (because the transistors are matched and on one chip).

Tell us what you have and we can, perhaps, help. An instrumentation amplifier can be made with three op-amps, and as I said, even a crappy 10-cent LM324 will be better than trying to use discretes. 



In general, an LM324 will probably drift about 5-10uV/K so you can expect (at best) errors commensurate with that- about 5g ~ 10g/°C. A better amplifier would reduce those errors. 

By comparison an B-E junction (as in your voltage follower) changes -2mV/K so you'd see 2kg/°C change- worse than useless.