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.
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.