Batteries are all over my place

Since 4 months ago when I started using solar panels as source of my electricity, I have bought a lot of batteries of different sizes and capacities. Batteries are very important because when you are not home during the day, you will need to store the energy captured by the solar panels so that you can watch tv and use your electric fan not to mention the power needed for your ligting needs. I also encountered several problems with these batteries because of their difference in s izes and capacities.

I noticed that when the 17ah battery is fully charged, I can use it to power my 29" Changhong LED tv for more than 2 hours but when I combine the larger batteries(26ah and 40ah) I still get 2 hours so I thought this is totally wrong. With 83ah, I should be able to use my tv 24hrs but I am not getting it. But that is what is happening and I think the basic explanation to this is that there are power losses maybe huge power losses when I connect the 3 batteries. The small ones acts as loads of the bigger ones and so while energy is consumed, the little ones competes with the actual loads(I am referring to the tv).

So to at least solve this problem and at least minimize the energy loss, I bought a 3amps ac-dc converter plus a mechanical timer to isolate my 28ah battery from the other 2 batteries so that when I come home at night, I can watch tv for at least 4 hours continiously and at the same time I can use my electric fan and lights without draining the batteries when I wake up in the morning and my theory has worked so far.