Spanish–English bilinguals rarely code-switch in the perfect structure between the Spanish auxiliary haber (“to have”) and the participle (e.g., “Ella ha voted”; “She has voted”). However, they are somewhat likely to switch in the progressive structure between the Spanish auxiliary estar (“to be”) and the participle (“Ella está voting”; “She is voting”). This phenomenon is known as the “auxiliary phrase asymmetry”. One hypothesis as to why this occurs is that estar has more semantic weight as it also functions as an independent verb, whereas haber is almost exclusively used as an auxiliary verb. To test this hypothesis, we employed a connectionist model that produces spontaneous code-switches. Through simulation experiments, we showed that i) the asymmetry emerges in the model and that ii) the asymmetry disappears when using haber also as a main verb, which adds semantic weight. Therefore, the lack of semantic weight of haber may indeed cause the asymmetry.