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What is the best filament that has the best strength to weigth ratio?

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I have not conducted an extensive study of this though I imagine that filament with carbon fiber is up there for FDM printers. For pure plastics my current understanding is that certain variants of nylon are among the top performers. It may be good to clarify if you are looking for high toughness or high yield strength.

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Carbon fiber adds weight and reduces flexural and tensile modulus. Carbon fiber only increases modulus or stiffness of materials (with the possible exception of the markforged with continuous CF infusion which is a branch of FDM)

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There isn’t generally a single material that is stronger in every category than other materials or a way to apply weight into that?

There are filaments that are stronger in flexural strength, tensile strength, modulus. There are higher and lower density filaments and different fills to increase or decrease density.

Do you have a specific application or application question or a specific strength/weight ratio needed?

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Like SOC3D already said, there is no single filament that outperforms all others in all areas.

My first question would be: Define ‘STRENGTH’

For example, PLA is often quoted to be less strong than ABS. Yet, with most brands of filament, the tensile strength of PLA is higher than that of ABS (and most other 3D filaments as well).

As the same time, flexible materials like Flexifil have a low tensile strength, but you will be hard pressed to break apart a thin sheet of 3D printed Flexifil-material because it will stretch a long way without breaking.