I want to purchase a bike lock which I can break easily if it gets jammed, preferably without any tool(or a very small/light tool which I can carry in my bag-pack). I have tried two locks and both of them jammed after some time. Also, they are really heavy which I don't like. I don't have much of a threat of a bike stealing where I live and just want to keep locks for my mental peace. But after having past experiences and getting the locks jammed, I really want to buy a lock which I can break easily. Please recommend. Thanks.
I suspect your question is framed from the point of view of your experiences. Any weak lock that can be defeated by a tool in your pocket can be defeated by the same tool anyone else carries.
Instead of wanting a lock that is weaker, you might consider a lock that is more robust, AND to perform periodic maintenance on the lock like you would with your bike. A routine oil does wonders to prevent crunchiness.
Consider buying a lock that has some way of shedding water, rather than collecting the water and rusting.
You might choose a lock with brass construction (brass doesn't rust) or perhaps stainless steel.
Another solution is to make sure the lock hangs in such a way that the keyhole is not facing upward.
If you really want a weak lock, get a velcro cable tie. It provides no security other than against a snatch-and-run. But its reusable, soft on the frame and won't scratch paint. You can also clip your helmet's chin strap around the forks and through a wheel. Security offered is basically zero.