For this problem, minimizing the absolute difference of group weights turns out to be equivalent to minimizing the maximum group weight, which you can linearize automatically as follows:

min MaxGroupWeight =
max(sum {i in ITEMS} weight[i] * Y[i], sum {i in ITEMS} weight[i] * (1 - Y[i]));
solve linearize;

Alternatively, you can do the linearization yourself manually by explicitly introducing a new variable and linear constraints as follows:

var MaxGroupWeight;
min Objective = MaxGroupWeight;
con Linearize1:
MaxGroupWeight >= sum {i in ITEMS} weight[i] * Y[i];
con Linearize2:
MaxGroupWeight >= sum {i in ITEMS} weight[i] * (1 - Y[i]);
solve;