Here is one way, although it is a little bit difficult to show in a simple sketch. Sorry, but the cross section sketches show the joints horizontally instead of in vertical orientation. Give me some feedback if this is not clear enough.:
The legs do not have to be 4" to support the weight, but they may be needed to get the 4-way intersection to work.
Two legs in one plane act as the primary assembly and are lap-joined with a notch in each leg to allow them to cross each other.
Next the opposite legs do not cross through. Instead create a 90 degree joint with a spline (dashed line) centered in each leg to support the 90 degree bend. (Shown in red). These legs will set in a mortise cut (not shown & narrower than the full leg width) into the sides of the primary legs (black lines).
A section through the combined legs is shown below.
The primary and secondary legs can be joined in a glued joint provided the boards are in good contact with each other. Otherwise consider some through dowels to reinforce the joints. I strongly suggest that you make a test model before attempting this for the actual project. There are bound to be complications that you did not consider that can be worked out in a test.