In the current landscape of language model research, larger models, larger datasets and more compute seems to be the only way to advance towards intelligence. While there have been extensive studies of scaling laws and models' scaling behaviors, the effect of scale on a model's social biases and stereotyping tendencies has received less attention. In this study, we explore the influence of model scale and pre-training data on its learnt social biases. We focus on BERT -- an extremely popular language model -- and investigate biases as they show up during language modeling (upstream), as well as during classification applications after fine-tuning (downstream). Our experiments on four architecture sizes of BERT demonstrate that pre-training data substantially influences how upstream biases evolve with model scale. With increasing scale, models pre-trained on large internet scrapes like Common Crawl exhibit higher toxicity, whereas models pre-trained on moderated data sources like Wikipedia show greater gender stereotypes. However, downstream biases generally decrease with increasing model scale, irrespective of the pre-training data. Our results highlight the qualitative role of pre-training data in the biased behavior of language models, an often overlooked aspect in the study of scale. Through a detailed case study of BERT, we shed light on the complex interplay of data and model scale, and investigate how it translates to concrete biases.