The term we use in this situation is "progressive overload", or lack thereof.
Yes, your body can adapt to one single movement at one single level of intensity. For instance, some people are able to do 100 pushups, but unless they add some sort of variety (increased weight, differing techniques), they won't be getting stronger from it. Their muscles have simply adapted to this particular routine.
It's like if your math class consisted of solving 2+2 all day. You're doing work, but how much is your math skill progressing?
We introduce progressive overloading into our routines in order to gain strength. This means that we can do the same exercise over and over, but we take measures to make sure that the muscles are stressed differently every time.
It can be, as in your example, increasing the weight with regular intervals. It can also be changing the set/rep scheme.
Now, if you do the same 6-7 exercises for years, you might be missing out on certain muscles. This is often solved by switching out certain exercises every now and then. Again, this variety lets our muscles experience different strokes, so they don't become too complacent.
Also note that "increasing the weight every 2 weeks or so" also has its limits. Obviously, we can't do this forever either. Which is another reason why we turn to variety.