I don't know what width your rims are (internal or external). If they are pretty narrow, you might have to run the wider tires at higher pressure than would be ideal for traction and comfort on trails. Otherwise they end up "floppy" under sideways forces, like during cornering or pedaling out of the saddle.
Another thing is: does the frame have clearance for wider tires? Seatstays, chainstays, any braces near the BB? I recall that Mountain Kings are not all that fat, for the nominal width, but I think they are significantly bigger than your stock tires.
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