Multiwall WS2 nanotubes (and fullerene-like nanoparticles thereof) are currently synthesized in large amounts, reproducibly. Other than showing interesting mechanical and tribological properties, which offer them myriad applications, they were recently shown to exhibit remarkable optical and electrical properties, including quasi-1D superconductivity; electroluminescence and a strong bulk photovoltaic effect. Here we show that using a simple dispersion-fractionation technique, one can control the diameter of the nanotubes and move from pure excitonic to polaritonic features. While nanotubes of average diameter >80 nm can support cavity modes and scatter light effectively via a strong coupling mechanism, the extinction of nanotubes with smaller diameter consists of pure absorption. The experimental work is complemented by finite-difference-time-domain (FDTD) simulations, which shed new light on the cavity mode-exciton interaction in 2D materials. Furthermore, transient absorption experiments of the size-fractionated tubes fully confirm the steady-state observations. Moreover, we show that the tools developed here are useful for size control of the nanotubes, e.g. in the manufacturing environment. The tunability of the light-matter interaction of such nanotubes offers them intriguing applications such as polaritonic devices, photocatalysis and multi-spectral sensors.