Wow! Six weeks! That's going to be hard. What kind of plants? How often do they need water? How big are the pots? If you have a faucet on your balcony, problem solved. Set up a drip system and use an irrigation timer to turn the water on and off.
If no faucet, there are drip systems you can set up using either a reservoir and a lot of irrigation tubing or a wicking system. I've done both and they work well but you might need a really big reservoir.
Nice fish. Was that supposed to be a photo of your balcony?
Daisy