Not わずかに, but しか does get a negative verb at the end while maintaining a positive meaning.
There is a pattern: しか＋ないverb meaning "only something" (positive sentence). eg:
この学校で田中さんしか知らないです。- I only know Tanaka-san in this school.
朝ごはんは、トーストしか食べなかったんですよ。- I only had a toast for breakfast.
For further reference.
So if we breakdown the sentence
when following what could be called 'sentence form', そうだ means I heard/people say that.
雨が降るそうだ - I heard it will rain
when following a verb's masu-stem or an adjective's stem (remove い or な as appropriate), そうだ means it looks like/seems
雨が降りそうだ - It looks like it will rain
Next you have みたい
みたい（だ） is a more casual version of よう（だ） and both work basically ...
I think @Eiríkr Útlendi's answer gives a good general answer.
If we look at 私は魚を食べる specifically: if it's said without anything else, I would interpret it as an explanation of what the speaker does (usually) ("I eat fish (in general)"), because it's uncommon to say 私は if you are not generalizing.
If it's literally only 魚を食べる, I would think it's ...