Document matching with more priority to certain features than others

I am working on recommendation systems wherein I need to match the similarity of 2 users. Now, I know that I can use Tfidf vectorizer to calculate the the cosine similarity score between them. But, now suppose I have some features where I have different priorities for those features. So, for each feature there will be a different priority and the one with with higher priority will be checked first. So, when I get cosine similarity based on that feature, I will move on to the next feature and so on. How can I achieve this?

$$similarity = \frac{\vec A\cdot \vec B}{\Vert A\Vert\cdot\Vert B\Vert}$$
Now, if you multiply each component $$a_i$$ of $$\vec A$$ and $$b_i$$ of $$\vec B$$ with a weight $$w_i$$ you will get a weighted cosine similarity.
Which weights you should use depend on the application. If you have a ranking of your features $$\vec R$$ you could give $$\frac{1}{r_i}$$ or $$\frac{1}{r^2_i}$$ a try. The feature with rank 1 will have a weight of 1 in both cases. In principle any measure of feature importance will do as weights.