Tyvek is frequently used on new homes as an infiltration barrier. It has no insulating value. It is usually applied over framing or sheeting prior to installation of siding. It does make the house tight but you also need to understand that it works as part of a system that includes an inside vapor barrier and wall insulation. Without the vapor barrier and wall insulation moisture will accumulate on the inside interface of Tyvek wrap. Thats bad because it holds moisture in contact witht he building framing.
The bottom line is, I would only recommend Tyvek for new construction or additions where a complete system of vapor barrier, insulation and infiltration barrier is being applied; otherwise it does more harm than good.
I don’t know what your current insulation status is, but if you have standard 2×4 walls filled with fiberglass the R-value is about 11. 2×6 walls are R-19. To get the best insulation during installation of new vinyl siding, your should consider adding rigid foam insulation between battens. The battens can be applied right over your existing siding and the foam boards applied between. This will increase R-value of the wall and give you a flat surface to mount your new insulation. This would give you much more bang for the buck than Tyvek in your case. Keep in mind you will need to build up window and door jambs in depth to match the new siding elevation. This just means adding the depth of the battens to the existing jambs and remounting your old casings or installing new casings on that thicker window/door.
Have a great project and post back any questions.