The merit factor (MF) introduced by Golay has long been accepted as the standard criterion to evaluate and design binary sequences with good anti-multipath property in sonar, radar, and communication systems for its theoretical tightness and practical simplicity. In this paper, we first show that the MF is a biased anti-multipath performance evaluation metric in theory and, more importantly, is not a pertinent sequence design criterion in practice for most binary sequences of practical interest. Then we propose the weighted merit factor (WMF) based on a non-uniform weighting of the out-of-phase aperiodic autocorrelation function (ACF) that provides accurate measurement of self-generated interference for the constant amplitude complex-valued sequences and the nonconstant modulus ones. Based on the WMF, a list of "bad" (of low MFs) binary sequences (lengths 33-95) with better anti-multipath performance than the "best" (known) ones have been designed to verify its greater pertinence over the MF as a sequence design criterion for sonar, radar, and communication systems. Moreover, we extend the weighted correlation model of the WMF to the code-division multiple-access (CDMA) systems and propose the weighted cross- correlation factor (WCF) to evaluate the sequence set's multiple-access interference (MAI) rejection property in the context of multipath propagation. Theoretical analysis corroborated by simulations confirms that the WCF provides greater practical pertinence and analytical tractability over the current standard criterion.