Hey and welcome on community forums!
This is not a stupid question, rather a good one!
First, た、ている and ていた。
As you know Verb[ている] means a progressive action(I am eating 食べている), in those verbs case Verb[た] will mean a past(or more precise completed verb), however with a group of words ている doesn’t mean a progressive action, but a resultant state:
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Movement words:
来る(くる)帰る(かえる)行く(行く)
instead of coming, coming back, going will mean being at a goal of the movement.(the state of being there)
So ロンドンに来ている。 Means I am in London(I have come to London(and I am still there)) instead of I am coming to London.
ロンドンに行っている。 Means I am in London(I have gone to London(and I am still there)) instead of I am going to London.
ロンドンに帰っている。Means I am in London(I have returned to London(and not a surprise, I am still there ) -
the words that depict the change from one state to another(you can easily spot them by their English translations which include words like become, get, put etc like: become fat太る, become thin痩せる, to get fired up燃える, to get to know知る, to put on着る, to open 開ける, become になる.
So accordingly, instead of ~ing, their ている forms will mean states: to be fat, to be thin, to burn, to know, to wear, something is opened, something is.
Now to the verb[た]. The verb た simply means that something has happened in ONE POINT in time in the past(or if we want to be more concrete - it has been completed). But we do not have information about whether it was going on for some time, it is not important or we do not want to say.
So for verbs from 2:
太る - to grow fat
太っている will mean to be in the state of being fat and can be translated as “to be fat”,
太った is simple information that at some moment in past someone got fat, or in other words that growing fat took place; and since details are lacking depending on the context might still be fat or not[the change took place in some point in past] can also be translated “to be fat”
太っていた will mean that someone was fat for some time(the state of being fat was going on for some time in the past).
https://bunpro.jp/grammar_points/27
https://bunpro.jp/grammar_points/136
Now let’s move to modify nouns.
Somethingがある + Noun is example of the same thing which can be generalized for every verb, so I will quote the explanation from it:
[障害がある]人 - person [that has an injury]・person [with injury]・[injured] person
the phrase [Aがある] modifies(qualifies) the noun B([Aがある] therefore becomes RELATIVE CLAUSE), or in other words describes the noun, similar to the adjectives creating one bigger noun. Since in Japanese there are no relative pronouns (that, which etc), the phrase simply directly precedes the noun(also like an adjective) that is modified.
Relative clauses have some rules:
1.topic particle は cannot be used
2.subject particle が can be changed to particle の(this in a sense marks relative clause)
So, let’s come back to our 太る(and whole group verbs from 2!).
太る人 person that(who) gains fat
太っている人 person that(who) is (in state of being) fat
太った人 person that(who) got fat(and depending on context might be in state of being fat(person that is fat) which is generally the case)
太っていた人 person that(who) was fat(for some time in the past)
So between 太った人 and 太っている人 and similar, which one is better?
Both are ok.