Usually, tuning issues have to do with friction at the contact points, not so much the tension of the strings. Some great players use tiny strings with trems and lots of normal bending, and on a well-set up guitar, it can stay in tune.
If your guitar nut is cut for 9 gauge strings and you put 11's on the guitar, it may cause even more tuning issues because of binding at the nut. What guitar are you having tuning issues with and what type of tuners are on it?
My electric guitars that stay in tune the best are more or less mechanically terminated at the nut - one Steinberger with string ends right behind the zero fret, and two locking Floyd Rose trems. The guitars with traditional cut nuts and headstock tuners stay in tune better when I keep a decent amount of graphite in the nut slots. I haven't noticed changes in string tension making a difference.