Hashtag trends ignite campaigns, shift public opinion, and steer millions of dollars in advertising spend, yet forecasting which tag goes viral is elusive. Classical regressors digest surface features but ignore context, while large language models (LLMs) excel at contextual reasoning but misestimate numbers. We present BuzzProphet, a reasoning-augmented hashtag popularity prediction framework that (1) instructs an LLM to articulate a hashtag's topical virality, audience reach, and timing advantage; (2) utilizes these popularity-oriented rationales to enrich the input features; and (3) regresses on these inputs. To facilitate evaluation, we release HashView, a 7,532-hashtag benchmark curated from social media. Across diverse regressor-LLM combinations, BuzzProphet reduces RMSE by up to 2.8% and boosts correlation by 30% over baselines, while producing human-readable rationales. Results demonstrate that using LLMs as context reasoners rather than numeric predictors injects domain insight into tabular models, yielding an interpretable and deployable solution for social media trend forecasting.