Are you able to tell if it is a buffering issue (internet) rather than a memory issue (computer hardware) that is causing the problem? You mentioned your computer was so, so it was not clear if it was the internet connection or not.
If it is the internet connection, you might try rebooting your modem/router. If you are using WiFi, connect directly into your modem/router instead if possible. This will speed up your connection. If it is only happening with this one site, it could be an issue on their end too.
If everything seems slow, try rebooting your computer and keep what you open to a minimum. Just open your browser and go right to where you would watch a video. Does it still happen? You can also try using another browser.
One other thing, if you right-click the video there may be a save-as option that allows you to download it. This may be disabled, depending on their settings. Worth a try!
Hope that helps!