Here's my (rather proto-scientific, I admit - take it with a grain of salt) take of linguistic relativity / Sapir-Whorf:
There are two types of thought: verbal and non-verbal. Non-verbal thinking is messy, not fully reliable and quite costly, but we use it quite a bit in our everyday. That part of the thought shouldn't be affected directly by the languages that you speak, and it's potentially in large part biological. (And perhaps not too different from what chimps think.)
On the other hand, verbal thought is far more structured, and relies on the languages that you speak. This means that they will influence how you think in some situations, making some concepts and ideas slightly easier to reach depending on the language.
If my hypothesis is correct, then strong Sapir-Whorf (language dictates thought) is false, but weak Sapir-Whorf (language influences thought) is likely true.