This is the 9029th most frequent Japanese word.
浮き
"浮き" means "float" or "floating object" in English.
In this sentence, "浮き" conveys the idea of something being not tangible or realistic, metaphorically floating.
その話は少し浮き上がっているように感じる。
I feel that story is somewhat exaggerated or ungrounded.
In this case, "浮き" indicates a device used in fishing lines to signal bites and maintain the hook's position in the water.
浮きを使って魚を釣るのが楽しい。
Using floats to catch fish is fun.
Here, "浮き" refers to a floating device used for buoyancy.