Danno, if your tiller arms really are 1/16" you may well want to stiffen them up. We had tubing in a different application that was constantly bending under load. I don't know what the actual wall thickness was but rather than make new ones, after 'straightening' them once again we filled them with expanding foam. The type that you can buy in aerosol cans in most hardware stores. Result - no more problems with the arms bending under load.

I think that the foam actually sticks to the inside of the tube and turns the whole thing into an integral structure. I can't see why it wouldn't work if applied to tiller arms.