You asked if you "need" a D800... the answer to that is almost certainly no.
The next question is "will a D800 benefit me?" And the answer to that is more complex... The short answer is "probably not often, but for landscapes maybe."
*IF* you can use a low enough ISO (should be able to), AND you have very sharp lenses (?), AND you can use wider apertures like ≤ f/8 (?), AND you can use higher SS's/better technique (tripod/remote release/etc), THEN the recorded file should have better quality/benefits than just about anything else available (DSLR's). And THEN, if you use that to print/display larger than you can with the D600, you will likely see notable benefits.
If anything in the above chain is not optimal, then the potential benefits of the D8xx drop significantly. And I have shown numerous times that if you use a D8xx to do "exactly the same thing," and for smaller display/prints, there's very little to distinguish a D8xx image from a 12MP D750/16MP D4 image.
Even when some of the chain fails, there can still be *some* benefit to a D8xx image file.... i.e. at minimum ISO there isn't much that can record/recover as wide of a DR, even if the image doesn't take advantage of the resolution potential.
You said you shoot primarily weddings and landscapes. In that case I do think a D8xx is a good addition to your D600, but I don't think it should relegate the D600 to "backup status." They are different tools and in many cases the D600 will work just as well, possibly even better (if only for the smaller files).
