I just got my 3DS back from repair. They removed the batteries, resulting the system time to reset. When I started the game, my town was filled with weeds, and it was fall. I asked Isabelle to change time, but the weeds were still there. After a few days, I recovered my town to a better state. But now, the system time remains still at January 2011. I want to change it, but I'm worried about having weeds in my town again. How can I change system time without affecting ACNL time?
You cannot change the system time without affecting ACNL time. You should have changed your system time to the proper time before starting the game up again the first time or at least before you picked all of the weeds.
What you can do to prevent the most headache is change your town ordinance to Beautiful town so that it minimizes the number of weeds that appear. Although over 2 years it might fill up anyway. Then you can hire Leif to pick weeds each day. Leif can pick a lot at a time so you should easily be able to keep up. It'll take a while again but it is not the end of the world. Leif sells this service only after you have upgraded Nook's to at least T.I.Y. though.
Now you know for next time.
P.S. Thinking about it, if you ACNL time is actually correct (as in today's actual date) through changing it through Isabelle, changing you system time will affect your ACNL time but it also might only change it to whatever your system time is, which will be the same as it is now and therefore you wouldn't time travel at all.
Or it will change it relative to your system time in which case you'd have to time travel twice. Once to align your system time with ACNL and once to align ACNL with real time.
So, in conclusion, you very likely have to time travel but you might get lucky.
you should try changing your system setting date and then when you click on your characters profile tell Isabelle "I need help first..." before starting up your file. Change the date to the exact same date that you set your system setting date for. Afterwards, start your file. (I have not tested this, however, It's your best bet for fixing the date without messing up the game because it does not auto-save your progress in the game until you tell Isabelle to start up your file.)