Don't throw out water!
Firstoff, you really need to not throw out liquids. Liquids should go down the sink, (unless they are non-water non-biological). Water based liquids are very heavy and add a lot of mass to the waste stream.
Water based liquids are particularly bad news when incinerating. Most trash will burn exothermically, meaning the incinerator only has to use fossil fuels to start the trash stream burning; once lit, the incinerator is sustained by the burning of the trash itself. Water is a different deal. Water does not burn, and every kilogram (pound) of water requires 349,000 joules (150 BTU) to warm it to boiling, and 2,260,000 joules (970 BTU) to boil it away, so that means they have to use a stupid amount of fossil fuel simply to boil away the water.
(the units in parentheses are the imperial version of that data; I am not saying 1kg=1lb nor 349kj=150 BTU).
It's worse. Water is a thermal moderator, i.e. it tends to absorb huge amounts of thermal energy while cooling things to 100C (212F) or below. So this is also cooling down the incinerator, and a cold-running incinerator runs dirty with incomplete combustion and throws a lot of HCs and particulates into the air. So to stay within EPA limits, the incinerator must crank up the burners, expending even more fossil fuel.
So if you have proper hygiene about your trash (throwing away basically dry stuff, using the sink drain for the wet), that removes the issue with paper bags.
Or have plastic bags just for the wet trash, and paper for all the dry.
Or consider non-fossil-fuel bags
Plastic is made from oil. Most plastics are made from petroleum (The Shah of Iran, very impressed with plastics manufacture, was astonished that we burned such a useful feedstock). Some bags are made out of organic oils, which works too. This "closes the carbon cycle", because you aren't digging up ancient carbon and adding it to the atmosphere, you are taking crop carbon that only came out of the atmosphere this year.