Researchers have proposed weighted frequent itemset mining algorithms that reflect the importance of items. The main focus of weighted frequent itemset mining concerns satisfying the downward closure property. All weighted association rule mining algorithms suggested so far have been based on the Apriori algorithm. However, pattern growth algorithms are more efficient than Apriori based algorithms. Our main approach is to push the weight constraints into the pattern growth algorithm while maintaining the downward closure property. In this paper, a weight range and a minimum weight constraint are defined and items are given different weights within the weight range. The weight and support of each item are considered separately for pruning the search space. The number of weighted frequent itemsets can be reduced by setting a weight range and a minimum weight, allowing the user to balance support and weight of itemsets. WFIM generates more concise and important weighted frequent itemsets in large databases, particularly dense databases with low minimum support, by adjusting a minimum weight and a weight range.