Intervals have been generated in many applications (e.g., temporal databases), and they are often associated with weights, such as prices. This paper addresses the problem of processing top-k weighted stabbing queries on interval data. Given a set of weighted intervals, a query value, and a result size $k$, this problem finds the $k$ intervals that are stabbed by the query value and have the largest weights. Although this problem finds practical applications (e.g., purchase, vehicle, and cryptocurrency analysis), it has not been well studied. A state-of-the-art algorithm for this problem incurs $O(n\log k)$ time, where $n$ is the number of intervals, so it is not scalable to large $n$. We solve this inefficiency issue and propose an algorithm that runs in $O(\sqrt{n }\log n + k)$ time. Furthermore, we propose an $O(\log n + k)$ algorithm to further accelerate the search efficiency. Experiments on two real large datasets demonstrate that our algorithms are faster than existing algorithms.