Virtual output queues (VOQs) is widely used by input-queued (IQ) switches to eliminate the head-of-line (HOL) blocking phenomenon that limits matching and switching performance. It has been shown that IQ switches can provide 100% throughput under admissible traffic when using maximum-weight matching schemes or iterative maximal-weight matching schemes with a speedup of two or more. These different approaches require either a high computation complexity or large resolution times for high-speed switches. Therefore, there is a need for lowcomplexity and fast matching schemes that provide high throughput under several admissible traffic patterns, including those with nonuniform distributions, without recurring to speedup nor multiple iterations. We proposed earlier weightless matching schemes based on the captured-frame concept for IQ switches to provide high throughput under uniform and nonuniform traffic patterns, when using a single iteration and no speedup. In this paper, we proposed to use the capture-frame concept in weighted matching schemes and show that performance improvement can be achieved. We apply this concept to the longest-queue first (LQF) selection to create the unlimited LQF (uFLQF) schemes. We show via simulation that uFLQF achieves high throughput under uniform and nonuniform traffic patterns with a single iteration.