Two things affect flow-
1. Pressure (or in this case, negative pressure, or "suction")
2. Volume of the hose/pipe (volume=diameter)
These are akin to the following in electricty:
1. Amps (pressure)
2. Volts (volume)
The reason I point this out is to make the point that, while you can increase the volume that you can potentially suck out of a tank by increasing the pipe diameter, the real factor involved in producing HIGH suction is the "draw" one puts on the pipe. In electricity, this "draw" is placed on a wire. Both the larger pipe and the larger wire can carry more "volume" (volts, or GPH), but it is only the draw that is variable.
So, with a tube/hose, you should also try to consider increasing the difference in height of the main water volume (tank) and the exit of the hose.
An extreme example would be a garden hose going down the side of a 4 story building- the suction would be incredible, and therefore the speed of water (GPH) would be maximized. Compare that to the same hose dropping water only 2 feet, and there would be a huge difference in GPH.
My point is, yes a bigger hose will help, but so would increasing the drop length, if you can, of the hose outlet. So if you buy something new, make sure it is long enough to utilize all of the "drop" you have.