I know the literal meaning is "to make the conversation/talk larger" but in terms of nuance of actual meaning in English I am confused. How would you say this in English?
2 Answers
「話{はなし}を大{おお}きくする」 is a set phrase meaning "to stretch a story", "to exaggerate", etc.
The fine nuance intended is context-dependent, but the expression is most often used to describe how better, worse or more important someone is trying to make his story seem.
The common contemporary and colloquial version would be 「話を盛{も}る」.
According to the dictionary 大きい can mean "exaggerated", "boasting", "bragging"
Examples:
できもしないのに大きい口をきく。
Even though he is unable to do it, he boasts about it.
大きい顔をする。
To be arrogant.
大きいことを言う。
talk big
おおきい【大きい】:
９ 大げさである。
10 いばっている。偉そうだ。
https://dictionary.goo.ne.jp/jn/28431/meaning/m0u/大きい/
https://dictionary.goo.ne.jp/word/en/大きい/#je-7796
So 話を大きくする means to "to boast", "to brag", "to exaggerate", "to talk big"
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「話を大きくする」は to exaggerate,「誇張する」「大げさに言う」「話を膨らます・盛る」って意味ですけど、to boast, to brag, to talk big,「自慢する」って意味ではないです。– chocolate ♦Commented Sep 29, 2018 at 14:31