Large background images – use different ones for different resolutions?

I am wondering, is it standard practice to have different versions of a background image per resolution switched out by CSS?

I wanted a background image that would look good on even the biggest screens, but it was coming out at about 600kb. I was able to reduce it to 2650x1920 and it's down to 300kb, but that's still a little big. As most users won't even need that high, would it be smarter to make an image at a lower resolution and swap that out with CSS depending on screen size? Is this standard practice or not usually done (seems like it could be more difficult to maintain).