The heavier you the person is on the rebounder, the more a stable the rebounder will be if it has a heavy gauge frame. The Cellerciser has the heaviest gauge frame of all the rebounders I have tested.
I do NOT recommend frames that don't fold unless only doing the Health Bouce. If jumping high on a rebounder with a non folding frame, they can warp over time and absorb too much of the shock when jumping high.
The bounce with a folding rebounder feels much better to most people. The folds break up the stress from the ballistic impact. The biggest problem is warpage. Many people have to put a piece of newspaper under one of the legs when this happens. Plastic frames are the worse when it comes to warping and aluminum frames have the second biggest problem. I always prefer a heavy gauge stainless steel frame. If you are going to get a steel frame, make sure it is robot welded from start to finish. When they are hand welded like most of the companies, the frame might not be 100% even and it can be just slightly off center. Most people fix this problem by not screwing in some of the leg all the way so the leg height make up the difference for an unbalanced frame. This will destroy the leg attachment and make it very difficult to screw off the leg or put it back on.
A final word on rebounder frames:
The more folds the rebounder has the sturdier and more grounded the bounce will feel. The trifold Cellerciser has the most stable feel with lightweight people but heavier people find the half fold more comfortable. The lighter a person is the more they will appreciate the breaks in the frame.

Note: the new Cellerciser has offset suspension where the springs are not directly hooked into the frame. Most springs hooks break when they rub directly into the frame and get hot. Having longer hooks can hale absorb the heat. Cellerciser has very small high gauge hooks that go into pins that the pins go into the frame. This makes it less squeaky. The Lymphaciser has corrogated rods welded into the frame which is totally different.
Note: I avoid rebounders that have punched/drilled in holes where the springs hook into the frame. (Offset type springs).

If you are looking for a frame that can support your weight and you are concerned about the rebounder being stable, let me know on my rebounder quiz.
First and foremost, I avoid any plastic frame or any frame that has been spray painted. Most frames out there are just spray painted and the paint can flake off over time. Electrostatically applied paint is the paint I recommend. Some rebounder frames are VERY hard to close and often requires 2 people to close or open it. Some are like giant bear traps and can be very dangerous if it catches you due to a hinge that shuts very forcefully.
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