Usually the research reactions are run very dilute as you noticed. So on scale-up you would try to make things much more concentrated.
The ratio of starting materials, usually remains the same, or gets better. Lots of lab experiments are run to optimise a reaction, and there are lots of parameters to look at. It really depends on the reaction. Work-up becomes crucial and things should crystallise, no chromatography but even that can be done , at least in the Pharma business where costs of product are not limited.
But I have gone from mg to kg and it's good fun.