Over-constrained problems can be solved with the help of soft constraints. Weighted constraints are a typical representation of soft constraints used to minimize weights of unsatisfied constraints. A natural extension of the CLP(FD) approach is presented which allows handling of weighted soft constraints. To achieve this goal, the costs associated with unsatisfied constraints is accumulated for each problem variable and its value. For the approach proposed, implementation of the soft constraint solver on top of the existing CLP(FD) library of SICStus Prolog is described. A large scale timetabling implementation demonstrates practical application of the approach presented.