Given the profound societal impact of conspiracy theories, probing the psychological factors associated with their spread is paramount. Most research lacks large-scale behavioral outcomes, leaving factors related to actual online support for conspiracy theories uncertain. We bridge this gap by combining the psychological self-reports of 2506 Twitter (currently X) users with machine-learning classification of whether the textual data from their 7.7 million social media engagements throughout the pandemic supported six common COVID-19 conspiracy theories. We assess demographic factors, political alignment, factors derived from theory of reasoned action, and individual psychological differences. Here, we show that being older, self-identifying as very left or right on the political spectrum, and believing in false information constitute the most consistent risk factors; denialist tendencies, confidence in one's ability to spot misinformation, and political conservativism are positively associated with support for one conspiracy theory. Combining artificial intelligence analyses of big behavioral data with self-report surveys can effectively identify and validate risk factors for phenomena evident in large-scale online behaviors.