I agree with Preston Botter that this is an advanced application of IRT. 

However, I am aware of a possible realisation. The `R` package `TAM` provides a *(not officially supported/documented)* solution for this issue using the so-called Q-matrix (quite possible that the following idea works for other software packages as well).

First note that in case of the 2 parameter logistic model the loading structure of the factor (discrimination parameter in IRT) is estimated in order to best fit the data. More importantly, in other words the discrimination parameter (B-matrix in `TAM`) is the relative weight of the respective item in the total score. 

Next, the Q-matrix is typically used as a **binary** matrix for asigning the loading of items to different latent dimensions. However, in `TAM` it is possible to assign values other than one to the Q-matrix. The values of Q are **multiplied** to the faktor loadings (discrimination parameter in IRT; 1 in case of the Rasch model). 

    > library(TAM)
    > data(data.sim.rasch)
    > data.sim <- data.sim.rasch[, 1:15]
    > head(data.sim)
         I1 I2 I3 I4 I5 I6 I7 I8 I9 I10 I11 I12 I13 I14 I15
    [1,]  1  1  1  1  1  1  0  1  0   1   1   0   0   1   1
    [2,]  0  1  0  0  0  1  1  1  0   1   1   1   1   1   0
    [3,]  1  1  1  1  1  1  1  1  1   1   1   1   1   1   1
    [4,]  1  0  1  1  0  1  1  1  0   0   1   1   1   0   0
    [5,]  1  1  1  1  1  1  1  1  0   0   1   1   1   1   1
    [6,]  1  1  1  0  0  1  0  0  0   0   0   0   0   0   0
    > mod1 <- TAM::tam.mml(resp = data.sim,
    +                      Q = data.frame("Loading" = c(rep(.5, 5), rep(1, 5), rep(2, 5))),
    +                      verbose = FALSE)
    > mod1$item
        item    N      M   xsi.item AXsi_.Cat1 B.Cat1.Dim1
    I1    I1 2000 0.8270 -1.6257163 -1.6257163         0.5
    I2    I2 2000 0.8145 -1.5382826 -1.5382826         0.5
    I3    I3 2000 0.8000 -1.4422434 -1.4422434         0.5
    I4    I4 2000 0.7860 -1.3542285 -1.3542285         0.5
    I5    I5 2000 0.7725 -1.2731382 -1.2731382         0.5
    I6    I6 2000 0.7710 -1.3979913 -1.3979913         1.0
    I7    I7 2000 0.7430 -1.2253834 -1.2253834         1.0
    I8    I8 2000 0.7435 -1.2283610 -1.2283610         1.0
    I9    I9 2000 0.7295 -1.1462542 -1.1462542         1.0
    I10  I10 2000 0.6945 -0.9509658 -0.9509658         1.0
    I11  I11 2000 0.6905 -1.2062157 -1.2062157         2.0
    I12  I12 2000 0.6615 -1.0102233 -1.0102233         2.0
    I13  I13 2000 0.6515 -0.9443237 -0.9443237         2.0
    I14  I14 2000 0.6415 -0.8791659 -0.8791659         2.0
    I15  I15 2000 0.6000 -0.6152801 -0.6152801         2.0

A word of caution: I'm not sure of what will happen if both relativ loading structure via Q-matrix are given **and** discrimination parameter are estimated.