Læreren lægger ekstra vægt på, at vi afleverer opgaven til tiden.

Yes, literally it is something like lays/puts weight on, but as a fixed expression it means emphasizes, places importance on, or attaches importance to.

So lægge vægt på is an idiomatic phrase. Danish often uses this expression where English would simply say emphasize or care a lot about.

• Læreren lægger vægt på det = The teacher emphasizes it / considers it important
• Læreren lægger ekstra vægt på det = The teacher puts extra emphasis on it

Because lægge vægt på is the standard expression. The preposition på belongs to the phrase.

You can think of it as:

• lægge vægt på noget = place importance on something
• lægge vægt på, at ... = place importance on the fact that ...

So after på, you can have either:

• a noun phrase: på opgaven
• or a clause: på, at vi afleverer opgaven til tiden

This is something you mostly have to learn as a set phrase.

No. Here at means that, not to.

In Danish, at can have two different jobs:

1. Infinitive marker:
   at læse = to read

2. Subordinating conjunction:
   jeg ved, at han kommer = I know that he is coming

In your sentence, it is the second type. It introduces a subordinate clause:

• at vi afleverer opgaven til tiden

So here at = that.

Because this is a subordinate clause, and Danish subordinate clauses normally use subject + verb order.

Main clauses in Danish often follow the V2 rule, where the finite verb comes second:

• I dag afleverer vi opgaven
  Here the verb afleverer comes before vi because I dag is in first position.

But after a subordinating word like at, Danish usually does not use V2 word order. So you get:

• at vi afleverer opgaven til tiden

That is the normal subordinate-clause pattern.

Because Danish often uses the present tense for something that is expected, planned, or required in the future.

So at vi afleverer opgaven til tiden does not have to mean we are handing it in right now. It can mean that the teacher cares that we do hand it in on time.

This is very natural in Danish, just as English sometimes says:

• It is important that we hand in the assignment on time

Danish does not need a special future form here.

These are similar, but not identical.

• til tiden = on time, at the correct or agreed time
• i tide = in time, before it is too late

In this sentence, til tiden fits because the idea is meeting a deadline or being punctual with submission.

Compare:

• Vi afleverer opgaven til tiden = We hand in the assignment on time
• Vi nåede at aflevere opgaven i tide = We managed to hand in the assignment in time / before it was too late

So for deadlines, til tiden is often the more direct choice.

Because it refers to a specific assignment that both speaker and listener are expected to know about.

In Danish, definiteness is usually shown by adding an ending to the noun:

• en opgave = an assignment
• opgaven = the assignment

So opgaven tells you this is not just any assignment, but a particular one.

It shows the common Danish pattern of adding the definite article as an ending.

• en lærer = a teacher
• læreren = the teacher

Unlike English, Danish often puts the at the end of the noun instead of using a separate word.

So both læreren and opgaven are good examples of the Danish suffixed definite article.

Yes, depending on the comma system being used.

Danish allows two official comma styles:

• with start comma
• without start comma

So both of these can be correct:

• Læreren lægger ekstra vægt på, at vi afleverer opgaven til tiden.
• Læreren lægger ekstra vægt på at vi afleverer opgaven til tiden.

Many learners see the comma before subordinate clauses very often, so the version with the comma is extremely common in teaching materials.

Yes. Aflevere is a very common verb for hand in, turn in, or submit, especially for schoolwork.

For example:

• aflevere en opgave = hand in an assignment
• aflevere lektier = hand in homework
• aflevere en rapport = submit a report

So in a school context, aflevere is exactly the verb you would expect.