have 3 fat people sit on it. If it holds, you don't need to strengthen it.
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Are those pull outs working or are they the nailed on. If they pull out it might be hard to brace it if the dont then a 2x4 subframe inside of it should work. It might even be sterdy enough not to have to reinforce it. Does it wobble or something?
If there's room for it you could put some 2x4's from top to bottom in between the drawers. That's if you dont mind haveing screws on the top of the cabinet. But it would help support the weight.