Where are weights stored in online applications?

I'm new to web development, so please excuse me if this question is trivial.

I have a background in machine learning, and am currently working on an application that involves various uses of machine learning techniques. When one is writing such an application, where are feature weights normally stored? The idea is that as users add data, the model will update feature weights to better learn the data.

Does one normally store feature weights in a database? How does one normally deal with this scenario? For example, suppose that I have a trained model and want to evaluate for a certain input. If feature weights are stored in a database, that requires looking up possibly several different values, which seems very computationally expensive.

What are the best practices for managing this?