In data fusion, the linear combination method is a very flexible method since different weights can be assigned to different systems. However, it remains an open question which weighting schema should be used. In some previous investigations and experiments, a simple weighting schema was used: for a system, its weight is assigned as its average performance over a group of training queries. However, it is not clear if this weighting schema is good or not. In some other investigations, different numerical optimisation methods were used to search for appropriate weights for the component systems. One major problem with those numerical optimisation methods is their low efficiency. It might not be feasible to use them in some situations, for example in some dynamic environments, system weights need to be updated from time to time for reasonably good performance. In this paper, we investigate the weighting issue by extensive experiments. The key point is to try to find the relation between performances of component systems and their corresponding weights which can lead to good fusion performance. We demonstrate that a series of power functions of average performance, which can be implemented as efficiently as the simple weighting schema, is more effective than the simple weighting schema for the linear data fusion method. Some other features of the power function weighting schema and the linear combination method are also investigated. The observations obtained from this study can be used directly in fusion applications of component retrieval results. The observations are also very useful for optimisation methods to choose better starting points and therefore to obtain more effective weights more quickly.