Owing to browser variation and differences in displays & end user settings, font rendering is NOT identical across all devices. That's the nature of the web.
With that in mind, font-weight is not pixel perfect either. It varies a lot by browser, platform (Win/Mac, etc...) and the pixel density of your display.
If your font has custom variants, it's not a bad idea to use them if it doesn't add too much excess bandwidth and negatively impact page load speed. Consult with your web developer about that. Nobody likes slow loading web pages.
Nancy O'Shea, Product User & Community Expert
Alt-Web Design & Publishing ~ Web : Print : Graphics : Media