adverb
carefully; thoroughly; deliberately
Used when someone does something with full attention, without rushing, or after careful consideration. Often appears in the set phrase とくとご覧あれ (take a good look).
この問題はとくと考える必要がある。
This problem needs to be thought through carefully.
とくとご覧あれ！
Behold! / Take a good look!
よく is a general adverb for 'well' or 'often'. とくと emphasizes deliberate, thorough attention and is less common in everyday speech.
じっくり means 'carefully' or 'taking one's time', similar to とくと, but とくと can sound more formal or emphatic.
The origin is uncertain. The kanji 篤 means 'sincere' or 'earnest', which fits the adverbial meaning, but the word is now treated as a lexicalized adverb usually written in kana.