Strength training is important for health, but conventional resistance exercise can feel repetitive or intimidating. Immersive virtual reality (VR) exergames may make strength training more engaging by combining physical movement with playful interaction. While rhythm-based exergames have shown motivational benefits, especially for continuous aerobic activities, less is known about whether music and beat synchronisation are beneficial for slower, form-focused strength exercises. We present BeatWeights, a VR dumbbell exergame in which players perform bicep curls while scooping and throwing fries to customers in a fast-food scenario. In a within-subjects study with 16 participants, we compared three one-minute conditions: synchronised music, non-synchronised music, and no music. Participants reported intrinsic motivation, perceived exertion, and muscle fatigue after each condition. Results showed a significant effect of condition on Interest/Enjoyment, with both music conditions rated more enjoyable than silence. However, synchronised music did not provide additional benefits over non-synchronised music, and no significant differences were found for perceived exertion or fatigue. These findings suggest that music can support affective engagement in short VR strength exergames, while precise beat synchronisation may be less critical for this exercise context.