Thanks a lot Canuck Physio

For your expert advice. There were quite a few aspects that I was totally unaware of, until I read your post.

When I was attending my physiotheraphy sessions, the physiotherapist prescribed exercises for just one leg. I guess that I had got it wrong about the part of using heavier weights to build more muscles on my weaker leg. Pardon me please.
The physiotherapist first asked me do a leg extension (one rep), using the max weight (about 60lb) and then she asked me to do the same on my left leg, on which I could only do like 20lb. So there was a difference of 20lb and since my left leg is way weaker, she told me to just concentrate on gaining strength on my left leg alone.

At this point, the weakness doesn't affect the way I walk though. I am not really able to see the physiotherapist regularly as the location is quite a distance from my place. But I do go to a gym located nearby with my cousin who helps me out. I was wondering whether I could attempt to improve my leg condition on my own for now rather than not do anything.

You had stated:

You could progress much more quickly if you were able to do for example a leg press machine with the aid of someone who can help you match your left sided leg weakness to the performance of your Stronger limb

I'll follow your instruction and work my stronger leg first and then focus on my left leg. So with my left leg if I can only lift a weight of 20lb, I'll stick to that and do lesser reps than my right?

Thank you so much for your reply and advice. Really appreciate it.