This is a little weired .. but.. here it is.
I have berber carpt in my living room and vinyl floor in the kitchen. The house has a basement. I always get this funny feeling that the floor is weak!!
You should get a apprehensive feeling not a funny feeling This is something that you need to have looked at right away. Is the ceiling in the basement finished?
If I just hop.. I get vibrations etc. I don't notice "weakness" that much in the formal dining room (I have padded carpet) there.
My guess is that you don't hop in the formal dining room. But that's just a guess.
Is there a way to "strengthen" the floor by giving some additional supports or some thing like that?
Yes. Very often this kind of problem is the result of water damage, or someone's "remuddling project" where a supporting joist was cut to make way for a pipe or ducting which weakens the floor. Both problems can be fixed and it would be well worth it to have an experienced carpenter do the work.
Thanks in advance..