Stutter can be caused by a busy server or if the video has a bitrate which is too high for the Chromecast to keep up. Especially on weekends the content providers are overloaded and can’t provide the videos fast enough. If possible try a SD stream instead of HD.
The Chromecast can’t buffer some streams at all and has a very small buffer. this might get fixed with a future Chromecast firmware update.
Don’t try to stream Blue-ray quality movies over WiFi. E.g. the Chromecast only supports 2.4GHz which is not enough to stream those movies. It won’t work.