More voltage make more current
All batteries have internal resistance according to their voltage and Ah capacity or rated by CCA or ESR.
But for a fixed load R, I=V/R so it is proportional.
But if you see inside a 9V battery is made from 6 tiny 1.5V cells the ESR is small to begin with for each cell then 6 in series adds resistance =  6*ESR.
But if you compare even a AAA battery is larger than the internal 1.5V in a 9V battery, so for the same chemistry and quality (e.g. alkaline, Panasonic), You expect the higher short circuit current on the lower voltage but bigger cell AAA battery than the 9V battery.
To make it clear more current with voltage is only linear if the R is constant.  Te example above shows adding tiny cells in series to make 9V increases R so that assumption is false.
ESR = Voc /Isc
Equivalent series resistance equals the open cicuit voltage divided by the momentary short circuit current.