Large language models (LLMs), while increasingly used in domains requiring factual rigor, often display a troubling behavior: sycophancy, the tendency to align with user beliefs regardless of correctness. This tendency is reinforced by preference-based alignment techniques that optimize for user satisfaction but can undermine truthfulness. While relatively benign in casual dialogue, sycophancy poses serious risks in high-stakes settings such as scientific question answering (QA), where model outputs may shape collaborative reasoning, decision-making, and knowledge formation. Despite its importance, this phenomenon remains underexamined in factual QA contexts. We address this gap by introducing a unified evaluation framework to quantify the impact of sycophantic context on model behavior in scientific QA, measuring how much user-imposed social pressure distorts model outputs. The framework incorporates adversarial prompting setups and targeted metrics, such as misleading resistance and sycophancy resistance, that capture a model's ability to maintain factual consistency under misleading cues. Systematic evaluations across open-source and proprietary models reveal pervasive sycophantic tendencies, driven more by alignment strategy than by model size. To mitigate this issue, we propose Pressure-Tune, a lightweight post-training method that fine-tunes models on synthetic adversarial dialogues paired with chain-of-thought rationales. These rationales reject user misinformation while reinforcing factual commitments. Experiments on challenging scientific QA benchmarks show that Pressure-Tune significantly enhances sycophancy resistance without compromising accuracy or responsiveness to valid feedback, offering a practical pathway toward more truthful and principled model behavior.