Are they SWEET basil?
S/B have big wide leaves and take long time to grow tall.
Also, if you have planted them as clumps, too close, then they will not grow as big.

You have to be patient . Few weeks is not too long for basil. It also depend on the weather. In cooler weather they grow very slowly.

Yes, I have two planted next to each other in a small pot. I will separate them into other pots. Can I plant them in pots in the size in the attached picture?

Also, approximately how long does it take until they start to grow taller? We are in warmer weather...

Thanks!

Yes, I believe its sweet basil. Yup, I have two planted next to each other in a small pot. I will separate them into other pots. Can I plant them in pots in the size in the attached picture?

Also, approximately how long does it take until they start to grow taller? We are in warmer weather...

Thanks!

OK. That pot is about right for one plant.

How long it will take ..???
If your daytime highs are 86F or higher, might take a month to grow about 10 inches tall. If temps are under 80F(+ cool nights)then it might take 6 weeks to grow 10". There are other varieties that grow taller, much faster. I have some Sweet Basils and Lemon Basils growing together, The latter is 3 times taller and I keep harvesting them. But Sweet basils are way low.. I sowed both at the same time.
Once it grows 3 nodes high, you can harvest above the second node. Then it will get bushy. The thing is that the heat of summer is winding down in most places. We will have, e.g., about 6-7 weeks of really warm summer. Then it will start cooling off. Basils by then will slow down.

Very helpful thank you.

When you say "above the second node", is the node the branch of leaves?

When you say harvest about the node, does that mean cutting where the leaves branch out and avoiding the stalk?

Thanks in advance, I'm really new to all of this!

OK. The 1st node is where the first pair of leaved grow.
The second node is where the second pair of leaves grow.
.... so on ...
From the upper sides of those leaves some potential branches can grow( as the plants get bigger).

When I say cut/harvest above the second node (or third node) I mean about 1/4" above it, leaving the leaves intact, the new branches (one from each side will grow just above the leaves. SO in effect the plant will have 2 stems.
After a while, as those branches grow several nodes, you do the same.. then the plant will have 4 branches... so on.
This is how to make basil bushy. Every time you harvest 1/3 of a branch (Not all of it) Then depending on the growing conditions you will have a bushy huge plant.
I must add that plants will do that (branching)on their own too but much later on. Some varieties naturally grow bushy, like GLOBE basil. Others, If you do not pinch/harvest, as I said, they will grow 2 to 3 feet tall(like some lemon basil).

But that is not your problem. It will take sweet basil a LONG time to grow real tall.