Let’s first look at examples in which the verb 置く is used in a literal sense.
The following sentences all mean different things as indicated in brackets.
- 台にテレビを置く。[habitual or future action]
- 台にテレビを置いている。[current state]
- 台にテレビを置いた。[past action]
- 台にテレビを置いていた。[past state]
They can be converted into the following noun phrases.
- テレビを置く台 [habitual or future action, or static property (in this case, purpose)]
- テレビを置いている台 [current state]
- テレビを置いた台 [past action or current state]
- テレビを置いていた台 [past state]
Of these, the one with the た-form (#3) is somewhat special in that it can also be understood as describing a current state just like the one with the ている-form (#2). However, it doesn’t quite sound so natural as, say, 太った猫, possibly because having a TV set placed on it is not so much a permanent property of the table as being fat is of the cat. It seems more natural to explicitly describe it as a state with the ている-form (#2) if that's what you mean.
When 置く is used in a figurative sense as in 重きを置く, it loses part of its quality as an action verb and this seems to blur the distinction between the two sentences below.
- うちの学校では特に語学に重きを置く。
- うちの学校では特に語学に重きを置いている。
Outside of limited contexts in which it is understood as describing a future action, the first sentence is no longer about an action but a current, or permanent, state of mind of the people running the school. Personally, the second still sounds more natural, though. This could be precisely because the possibility of 置く referring to a future action cannot be ruled out completely.
The following pair in the past tense also means practically the same thing as one another.
- 昔は徳育に重きを置いた。
- 昔は徳育に重きを置いていた。
Although I would still choose the second if I have to choose one, the naturalness of the first sentence seems to somewhat increase compared to the first sentence in the present tense above. Even if 置いた is understood as a past action, the state that resulted from it is already a thing of the past. Then, it is not much different from what the second sentence says.
As for the noun phrases, the following three are all correct.
- 聞くことと話すことに重きを置く言語獲得の体系
- 聞くことと話すことに重きを置いている言語獲得の体系
- 聞くことと話すことに重きを置いた言語獲得の体系
The version with the た-form (#3) sounds more natural than テレビを置いた台 probably because the described property of the system is more permanent. The version with the ている-form (#2) sounds slightly less natural than the other two to me because it makes the described property seem like a transient state.