。
The weather will probably get better tomorrow.
Literal
Tomorrow [possessive-の] weather [topic-は] become-good probably.
だろう is the plain-form probability/conjecture marker — the casual counterpart to でしょう. Attached to a verb phrase, it expresses the speaker's estimate that something is likely the case. 良くなる uses the adverbial form 良く + なる ('become') to mean 'to become good' — Japanese derives 'improve' from adjective + 'become' rather than a dedicated verb.