I lost some weight by running everyday and eating less
I managed to lose weight by going for a run everyday and eating less
(1) I lost some weight by running everyday and eating less
'lose weight' (過去形:'lost weight') =「痩せる」「体重が減る」
'~ by ~~' = 「~~することで~」
「毎日走って食事を減らすことで痩せたよ」
(2) I managed to lose weight by going for a run everyday and eating less
'managed to ~' =「どうにか〜する」「成し遂げる」
'go for a run' = 「走りに行く」「走る」
「毎日走りに行って食事を減らすことでどうにか痩せることができた」という意訳の訳出です。