When you calculate the estimate, say as the mean of some sample quantities, you should be able to get the variance estimate of the sample quantities also.
So for each of the estimate you give
estimate 0.85 | 1.05 | 1.57 | 3.36 | 3.88 | 3.63 | 3.50 | 3.97 |
Variance S1 S2 S3 ......
As a result, the weights for the eight estimate should be each calculated as W_j=(1/S_j)/Sum(1/S_k) , the sum is taken over all 8 estimates' variances.