The mMovie I wWatched rRecently

I watched a movie called "The Whale", t.” This movie shows a hitells the story aboutof a mean who is having weight problemsstruggling with his weight.

It is neater to separate this sentence into two.
I think by “history” you mean “story,” as the word “history” is used when referring to someone’s past or background.
“Weight problems” is not really a phrase used in English. You could say “struggling with his weight,” or to keep it closer to your original, “he has a weight problem.”

He started to gain a lot of weight becauseafter his boyfriend died, so he started to eat because he ate a lot to feel better.

Using both “because” and “so” to connect clauses in the same sentence sounds unnatural and wordy. Instead of “because” you could use “after.”
The repetition of “started” is not necessary, you can remove it from the second clause.

I watched a movie called "The Whale", t. This movie shows a history aboutthe life of a mean who is having weight problems.

He started to gain a lot of weight because his boyfriend died, sothen he started to eat a lot to feel better.

"Because" and "so" duplicate the "because" meaning here, so it's better to use "then"

I watched a movie called "The Whale", t. This movie shows a hithe story aboutof a mean who is having weight problems.

He started to gain a lot of weight because his boyfriend died, so h. He started to eat a lot to feel better.

I watched a movie called "The Whale", t. This movie shows a history about a mean who is having weight problems.

You can use "shows a" and it's technically correct, but it would be more fluid to simply say "this movie is about a man" instead.

You can also turn "who is" into "who's" to sound more native

He started to gain a lot of weight because his boyfriend died, so he started to eat a lot to feel better.

This is definitely how people speak in real life, so it's not wrong

Technically, in formal writing, you want to avoid using multiple joining words in a sentence (because, and, so, etc) as it makes the sentence less clear. But, this is only important if you're writing something formal

The movie I watched recently

This is not incorrect, but it would sound better if you said "A movie I watched recently"

I watched a movie called "The Whale", t. This movie showtells a history about a mean who is having weight problems.

He started to gain a lot of weight because his boyfriend died, so he started to eat a loteating a lot to feel better. (or even better: he started overeating to feel better.)

I'm not sure if this description of the movie is accurate, but it was the wayhow I interpreted the movie.