Depends on what your plans are for the bumper..
Hang bikes on it? Yeah, the heavier and reinforced the better.
No plans, original 1/16" would be fine..
Myself, used 1/8" wall square tubing because it is far easier to weld on without blowing holes in it than 1/16" would be.
1/16" is approx 14 gauge sheet metal thickness and that takes a pretty light rod and low amperage with stick or a decent MIG welder.
1/8" thickness welds very nicely with stick welder..
Downside to thicker wall is the inside dimension tends to get reduced so if you are planning to store the stinky slinky in there you better verify not only the hose fits but the bayonet fittings also. Most likely will not fit the bayonet fittings in 3/16" thickness tubing..
The plastic end plugs may also need some modifications to fit a thicker walled tube.
You won't be adding all that much weight, much less than say a bicycle.. Now if you were going thicker than 1/4" then you might have some issue but as long as you have no plans to mount something to the bumper I wouldn't go too much heavier than 1/8" just to keep the unneeded weight to a min..
