Definitely "by" -- the method or means by which you do something By eating less, you feel lighter and may lose weight. by + v+ing I would not use ' through' with a gerund (v+ing) but with a noun. People learn some things through repetition. BUT: People learn words in a foreign language by repeating them over and over. Another example: He learned to play this piano sonata by practicing every day. He learned to play the piano through daily practice.

'by' would be the most common preposition used. 'through' would work better with a noun phrase, e.g. ' Lose weight through the practice of running'

An English professor would probably answer "through", but to an average English speaker you can use either sentence and it would sound perfectly fine.

You need the preposition, "by" in your sentence. The word, through, also a preposition, can describe travelling from place to place. For example, "the train travelled through the tunnel" or "he walked through the doorway". It can be used to explain how water moves. For example, "the water soaked through the coat" or "the water went through the tap". The word can also be used to describe the end of something. For example, you could ask, "are you through with my pen" or "he is through with school for the year". Hope this is helpful

(By) It's preposition