The most important advantage of using open weights models is to have perfectly predictable performances and costs in the future. When you can run the model on your own hardware you are protected from price increases, subscription limits decreases or quality reductions of the provided models, like it has already happened for the users of Claude Code.
The disadvantage is that if you also want a high speed, you need more expensive hardware. You may defer the cost of buying better hardware, if you use an external provider for now, but you keep in reserve the possibility of hosting yourself the models that you are using, if anything makes the external providers worse.
That difference is actually pretty surprising. Is Claude that much more expensive to host? The end-user pricing seems to be pretty similar, or better for OpenAI.