Yup, bigger boats have bigger parts and greater forces. I went from a 26 footer to a Catalina 309 (31 feet). The winch handles definitely see more use. There's no way I could sail that boat without a handle (unless I was to actually excercise....a lot).
What you're talking about is normal. A 27 is less physically demanding. That said, there's no way I want my old boat back. Got used to sailing the 31 real quick. Goes faster and is more comfy. Wife likes it a lot more.
Got a spare winch handle?