Sending multiple queries from your web server will likely put more load on the database server than using a stored procedure.

With either technique you are still pulling all the data you need from the DB but with multiple queries instead of a stored procedure you are usually pulling more data than you need with each query and then dropping any rows or fields you’re not interested in. Together with multiple calls over the network to the DB server and (often) multiple SQL connection setups this is much worse for performance on both the web and database servers