It's crazy complicated. But:
If you are concerned with heat-loss due to evaporation, then reducing the exposed surface area will help. The rate of evaporation is proportional to surface area.
If you are likewise concerned with maximizing heat-gain from the sun, then that too is proportional to surface area.
Finally, heat loss due to convention is also proportional to surface area.
So everything you care about is strongly affected by surface area, thus maximizing the amount of water that is covered is a good goal.
It's impossible to estimate how important this will all be as far as actual water and heat loss/gain - you haven't given enough information in your question to judge that.
The unanswered question is how much heat and water loss your pool is experiencing, and what is preventing it from losing more. You might alter the rate of cooling/water-loss without actually affecting the ultimate final temperature and total water-loss.
Example: If I have a leaky bucket that I fill up with water once, it doesn't mater how quickly the bucket drains because once it's empty there isn't any more water to lose. If I am constantly topping up the bucket, then fixing those leaks is more important.
If I were you, I'd conduct an experiment. Leave the cover totally off for a few days and measure whatever you care about (water level, temperature, pool-heater-energy-consumption). Then do the same with the cover on, and perhaps again with the cover 1/2 on. That should give you enough information to make a gut decision on how much the pool cover is helping.
Answered by OP in comments:
I did it! There is something like a little groove at the side - at the connection between black and white parts - wherein I slotted a screwdriver, twisted it, and the light cover pulled off. Eureka! – Lukman Dec 17 '16 at 12:16
Best Answer
I just had to deal with that last week. On an expensive rundown timer, no less! The rectangle shape is Decora, and those outer screws hold Decora plate covers, which use an extreme outer position. You have two choices:
bend or hacksaw them off. Your device can never be used with a normal Decora cover plate.
dump the accursed raised cover (you certainly don't need the cubic inches) and go with a 1-gang mud ring for a 4" box. This is flush, but has a 1/2" extrusion the size of a 1-gang box. This has the space needed. And then you use a plain Decora cover plate, which needs those threaded holes. If you need dual Decora, they make 2-gang mud rings too.