2 more weeks than usual? or 2 weeks more than usual?

I have not edited your question because to do so would be to answer it without explanation.

The answer hinges on the use of more. More is a comparative and requires the comparison of two things. One is more than the other.

The first sentence of your question states that the time is two weeks compared to the normal time. You do not state the normal time; it may be bigger or smaller. The comparison is meaningless. The second sentence says the time is two weeks.

You then give sentences that use more to tell us that the time is greater than normal by two weeks. This clarifies the intention of your original but because you told us the time is two weeks, you are saying normal time is zero. This is unlikely!

Your first paragraph should therefore be corrected to read

“ABC company realized transit time currently takes 2 weeks more than the usual time. So they need to inform their customers that it will take them 2 more weeks to receive the goods.”

You could also use “... 2 weeks more to receive...”. As a native speaker, I am accustomed to both constructions. Either of your suggestions is acceptable.

It would be better to say 'two weeks longer than usual'. We can speak of 'two more weeks' in some contexts (I have two more weeks of holiday), but it doesn't sound natural here.