Yes, Alex has it right. How much frame flexing, both fore-to-aft and side-to-side frame flexing should you expect? It really depends on the frame of your truck and the year. Older Fords were made to have a lot of flex, especially the long wheel base models. The newer the truck the less frame flex you get, IMEX. My short wheel base Ram with a hydro formed frame and enough cross members has little flex; by design. I was starting to get some fore to aft 'rocking' and found that one of the four 3/8" bolts holding the bed onto the frame had pulled through the anchor tab and was floating. 3, 3/8" bolts holding the entire 2500 pound bed and TC to the frame of the truck. Scary. The other issues are your suspension and your shocks. I use the Lance struts. I still like the 14 yr. old ones I use on every trip. It just tightens things up, like too-small underwear. 8<) For porpoising, it's the best solution, ..so far. The pros and cons of Lance struts have been beat to death on here, mostly the nays are by people who have never had them, and the yeahs are principally by people who have actually used them. Just know this: they make some difference, but are not the do all; fix all for stability.
The other issues are your suspension and your shocks. I have done a lot of fine tuning to reduce the sway, pitch and yaw, and off-road is a whole different animal to deal with. Recently, I replaced the front and rear anti sway bar rubber, 4-link bushings and most of the Gen II steering components with newer Gen IV versions. This 15 year old truck is very tight now, almost like new. Why not like new? I would say the body bushings holding the cab and bed to the frame are getting tired. Am I going to address that? Nope, the next owner can deal with that issue.
To really address rocking and sway reduction the thing to do is get WAY more truck than you think you will need. A 4 or 5 series truck will keep you far from the wobbly situation you get with a low rated 2 series truck. Of course, there is no free ride. The ride in an MT 4 or 5 series will rattle your teeth, unless you get the new air ride. 8<)
jefe