In this paper, I propose that Probabilistic Grammar may benefit from incorporating theoretical insights from Cognitive (Socio)Linguistics. I begin by introducing Cognitive Linguistics. Then, I propose a model of the domain-general cognitive constraints (markedness of coding, statistical preemption, and structural priming) that condition language (variation). Subsequently, three case studies are presented that test the predictions of this model on three distinct alternations in English and Spanish (variable agreement with existential haber, variable agreement with existential there be, and Spanish subject pronoun expression). For each case study, the model generates empirically correct predictions. I conclude that, with the support of Cognitive Sociolinguistics, Probabilistic Grammar may move beyond description towards explanation. This article is part of the special collection: Probabilistic grammars: Syntactic variation in a comparative perspective