Large language models increasingly serve as conversational agents that adopt personas and role-play characters at user request. This capability, while valuable, raises concerns about sycophancy: the tendency to provide responses that validate users rather than prioritize factual accuracy. While prior work has established that sycophancy poses risks to AI safety and alignment, the relationship between specific personality traits of adopted personas and the degree of sycophantic behavior remains unexplored. We present a systematic investigation of how persona agreeableness influences sycophancy across 13 small, open-weight language models ranging from 0.6B to 20B parameters. We develop a benchmark comprising 275 personas evaluated on NEO-IPIP agreeableness subscales and expose each persona to 4,950 sycophancy-eliciting prompts spanning 33 topic categories. Our analysis reveals that 9 of 13 models exhibit statistically significant positive correlations between persona agreeableness and sycophancy rates, with Pearson correlations reaching $r = 0.87$ and effect sizes as large as Cohen's $d = 2.33$. These findings demonstrate that agreeableness functions as a reliable predictor of persona-induced sycophancy, with direct implications for the deployment of role-playing AI systems and the development of alignment strategies that account for personality-mediated deceptive behaviors.