To make this change is very simple and should take about 5 mins.
First download the 1.03 data files from 
hereNext unzip the contents, and copy the folder within it named "GameInfo".
Navigate to this location on your PC.
C:/Users/[username]/AppData/Local/Ironclad Games/Sins of a Solar Empire/Mods
Replacing [yourwindowsusername] with your windows user name. You may also need to set "show hidden files and folders" in the Folder Options control panel windows to see AppData.
Create a new folder in "Mods" called "SuperFleetSize".
Paste the "GameInfo" folder from the 1.03 data files into here.
Find the file called "gameplay.constants" within "GameInfo", then right click it and select "Open With" from the menu. Open it with a text editor such as WordPad.exe
Press ctrl-f and type in "fleet supply scalar" top find the entry for fleet supply. Change it to the following - 
fleetSupplyData-Small
		fleetSupplyScalar 
1.00	fleetSupplyData-Normal
		fleetSupplyScalar 
2.5	fleetSupplyData-Large
		fleetSupplyScalar 
5.00This will now mean that choosing normal or high fleet capacity will give you 2.5 and 5 times the default respectivly. You can edit these numbers further for larger/smaller caps.
When you enter Sins, go to the Options tab, then the Mods tab and enable the "SuperFleetSize" Mod.
When you start a game you will begin with 500 supply, and it should scale as you research it.
To upgrade Capital Supply Capacity is more difficult I think (unless I am missing something). You would need to edit the files (also in the "GameInfo" folder in the mod) - 
RESEARCHSUBJECT_MAXCAPITALSHIPSPHASE0 to 7
RESEARCHSUBJECT_MAXCAPITALSHIPSPSI0 to 7
RESEARCHSUBJECT_MAXCAPITALSHIPSTECH0 to 7
So that in all 24 files the part like this -
researchModifier
	modifierType "CapitalShipMaxSlots"
	baseValue 0.000000
	perLevelValue 1.000000
researchModifier
	modifierType "CapitalShipMaxSlotLevel"
	baseValue 0.000000
	perLevelValue 1.000000
has the figures perLevelValue and baseValue (only used in the initial research) have scaled up values, say like this
researchModifier
	modifierType "CapitalShipMaxSlots"
	baseValue 0.000000
	perLevelValue 
5.000000researchModifier
	modifierType "CapitalShipMaxSlotLevel"
	baseValue 0.000000
	perLevelValue 
5.000000Hope that helps.