Thought is neither determined by language nor independent of it. Even then, the relationship between them is strong.
The idea between Sapir-Whorf is that you cannot think something if you don’t have language-tools capable to express it. The classical example is Newspeak, the language of Orwell’s 1984. Newspeak had been designed to make the populace incapable of rebellious thought. Instead of the word /BAD/ Newspeak had only /UNGOOD/.
It is very difficult to measure the strength of language influence. But my guess is this: the person cannot think outside the categories provided by language. The reason is not that language causes thought, but rather that Thought and Language are both determined by the category-making activity of society.
That would be very close to supporting Durkheim‘s totemic-thought thesis, except that it is not the social life that acts on language. Instead, Language determines social Life. To make it simpler:
Language determines Life.
To be even more explicit: in a supposed “Eden” situation where language is being built from the ground up Language and Social Life interact in a feedback loop, without difference in strength of influence. But in every actual situation language is extremely more powerful than the social life.
The real question is that language is more abstract than life (at least by one order of magnitude). Therefore their fluxes of diversity will differ as linear to exponential. Arithmetic to Geometric progression. In any given moment Life can have stronger effects than Language, but in the long term Language will always overcome it.
So, back to Sapir-Whorf. Human thought is bound by it’s cultural patterns. The Culture is bound by the constraints of it’s main engine: Language.
Just one more example: in a teenage gang belonging-symbols (the red handkerchief, the black blouse with a skull, the spiked bracelets…) are used to synchronize behavior. If someone doesn’t have the symbol, a gang member will spank him. If he has, he will not. But if he has and the leader says he shouldn’t, he will be crippled. A symbol (language) is the deciding factor in the distribution of violence (life). Obviously it is not the handkerchief that is creating the situation, but the handkerchief-used-as-symbol, or more precisely not as much the bracelet but the symbol-of-gang, which will probably begin by a powerful sounding name, the very idea that a band of teens can become a gang, and THAT idea is only possible through a gang-symbol.