You have a few choices, Nancy, but not a million of them. And all of them will have a caveat: Short of getting a sit-on-top, which I dont think will work for the kind of paddling you want to do, you wont know what really fits until you go sit in one.
Necky Looksha V Kayak
But there are certainly boats designed for larger paddlers, and with the capacity to handle 400 pounds (boater and gear). One candidate would be the Necky Looksha V ($1,699 polymer/$2,999 composite; necky.com). Its whats described as a high-volume" kayak, meaning it has more interior room and is a little bit wider in the beam than most boats. Still, its known for easy paddling and good tracking, and a rudder helps with maneuverability. Necky doesnt list a total weight capacity, but its a big boat (over 17 feet), with roomy bow and stern hatches, so I shouldnt think 400 pounds would pose any real challenge to it, especially for lake paddling.
Better yet might be Wilderness Systems Tsunami 175 ($1,650; wildernesssystems.com). Its a roto-molded boat like the less-expensive Looksha, but it isnt quite as performance-oriented and is a bit wider and even more stable. The cockpit, in fact, is three inches wider and four inches longer than that on the Necky. Its rated to 400 pounds capacity, has a rudder, and comes with fore and aft stowage hatches as well as a small day" hatch right behind the cockpit. Plenty of room for multi-day trips.
Lastly, Perceptions Eclipse 17 Airalite ($2,400; kayaker.com) offers 425 pounds of weight capacity with a cockpit thats in between the Necky and Wilderness Systems boats. Its made from Airalite, a really wonderful material that offers the light weight and looks of composite boats but doesnt cost too much more than plastic.