I agree with @Preston Botter that this is an advanced application of IRT and support the advice that you might want to look for consultation. 

However, I am aware of a possible realization. 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 loadings (discrimination parameter in IRT) is estimated in order to best fit the data. More importantly, the discrimination parameter (B-matrix in `TAM`) is the relative weight of the respective items in the total score. 

Next, the Q-matrix is typically used as a **binary** matrix for assigning the loading of items to different latent dimensions. However, in `TAM` it is possible to assign values other than zero or one to the Q-matrix. The values of Q are **multiplied** to the factor loadings (discrimination parameter in IRT; 1 in case of the Rasch model). Thus, we can force a loading other than 1 to items in the Rasch model (or multidimensional versions thereof).

    > 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.