Yep, wider is not better on motorcycle tires, at least not without wider wheels to match.
Instead of a nice round cross-section and consistent smooth handling, you get a cross section more like a hamburger bun and spooky inconsistent handling.
That said, I believe a wider rear wheel is possible in a DL swingarm, and I know there are some who have put a 17" front on a DL (very, very bizarre looking). The overall effect on handling is questionable at best.
If you want your bike to handle better, here are the top three priorities. They cost money:
1) Learn how to ride better. Take a good class or three. You'll be a lot safer and you'll have a lot more fun. A good rider on a clapped-out bald-tired Tohatsu Runpet will outrun a wobbler on a racebike, every time.
2) Make sure your tires are always fresh. Replace them before they get squirrely, buy name brand tires appropriate for the surfaces you'll be riding on, and don't let them get more than a year or two old.
3) Pry open your wallet and invest a couple grand in premium suspension tuned to your weight and riding style and brakes. Springs, emulators, fresh oil, fork brace up front, premium shock out back. Install stainless braided brake lines all around and maybe upgrade the front calipers if you have weak hands.
2002 Suzuki DL1000 V-Strom, Dark Metallic Space Blue
1983 Suzuki GS850G, Cosmic Blue
2005 KLR685, Aztec Red - Turd II.2, the ReReTurdening