。
She gave me a suspicious look.
Literal
She [topic-は] suspicious-looking [adverbially-に] me [object-を] gazed-at.
疑わしそうに layers two patterns: the i-adjective 疑わしい ('suspicious, doubtful') gets the evidential ~そう ending ('looking like, seeming'), then the adverbial に turns the whole adjective phrase into a manner adverb. The literal meaning: 'in a manner that looked suspicious.' This 'i-adj minus い + そう + に' chain is hugely productive — 嬉しそうに ('looking happy'), 悲しそうに ('looking sad'), 恥ずかしそうに ('looking embarrassed'). It's the standard way Japanese describes another person's apparent emotional state without claiming direct access to their inner experience.