It would be nice to have something in the panel that would let us adjust hull, shield and weapon strength in stages up or down, but right now, modders are adjusting those values inside the ship files. So there is a way to do it, but not as easily as a button on a panel. If you have updated 1.05 with the first update that was issued in Febuary i believe, it will create a mod panel in the options area. From there, if you download the forge tools found on this site at the download page i believe, there are a number of tools available. Galaxy forge and Particle forge among them. Also, very importantly is a Reference folder with text versions of the files in the main part of the game, such as GameInfo, String, Mesh and Others. For now we can concentrate on the GameInfo folder as it holds the files we will need to change to do just what you want.
After downloading the forge tools and running the update(from febuary, the latest updates are for the beta for 1.1, that is something you may want, but not for this purpose at the moment. If you go to the Options folder and click on Show Path, the game will create a folder structure for the mod folder for you. C:\Users\Appdata\Local\IronClad Games\Sins of a Solar Empire\
Inside this folder you will see a variety of folders now.
AppData (On Vista) is usually hidden, but you can locate it, by going to search and typing appdata
For XP machines i believe it is Application Data instead.
Once there (in the Solar Empire folder) and create a folder in the mod folder that you want to make this new mod in. Lets say you call it, My First Mod, then go to where you downloaded the Forge Tools and locate the Reference Data folder and copy it to your Solar Empire folder. Then open it and copy the included GameInfo folder to the inside of your My First Mod folder. What we have now is a clean gameinfo folder with text readable files inside your My First Mod folder inside the Mod folder. 
Okie, now, open the My First Mod folder and the gameinfo folder inside it, i suggest setting the folder options to details as it will give you a line by line view of your files. From here, scroll down the list, it is alphabetical and starts with abilities, then buffs and other things. Get to the CapitalShips area, in the C's naturally.
Find your Halcyon Carrier, by looking for CapitalShipPsiHalcyonCarrier. Please notice the uppercase/lower case pattern of the filename. Open the CapitalShipHalcyonCarrier file with a double click, Windows will probably ask you to associate it with an application becaise it doesnt recognize it. If there is a browse window to associate the file with then click browse and go to C:\Program Files\Accessories and locate Notepad. Associate .entity files with Notepad for now. Once that is done, double click to open the file. Viola!! We now have an open HalcyonCarrier file we can read!
If you now go to several lines in the file below. The abilities for the ship are at the top. You can experiement with these later, but for now go past them to the weapon area below.
Carriers carry i believe 2 or 3 weapons. Projectile and Beam.
Note the values at the end of the lines for the lines FRONT, BACK, LEFT, RIGHT. these are the weapon strengths for guns mounted in the front of the ship or at the back, and to the left and right sides of the craft.
You can now change them. Most are below 100, some craft are slightly more, but usually very few. If you take the value and change it, say to 2000
then now you have a super weapon! For now leave the other values alone. You can experiment with them later. But just save your file, by going to file/save and then close the file. Close the mod folder and start up you game. At Options you will see a Mod button at the bottom, click it. Inside will be a list to your right, that should have your My Fist Mod folder name in it.
Click the button that says load. It will attempt to load. If we haven't messed things up, then it will load. When i first did this it took me about a half a dozen tries. I kept changing too many file values, i wanted to experiment with other things too. What i did in the end was change only that one value and then save it. Then i was okie. Now when it loads, go to New Game and select a game you want, click it and it will load the game. Inside get everything set up the way you normally do. Get your CapitalShip factory built and build your Halcyon Carrier. Now build some other support ships if you like, diciples, and a missionary and a couple of scouts if you like, now go test them. You could make your Carrier the leader of the small fleet and go the the nearest planet or asteroid, usually there are some small bands of bad guys there. Attack,
your Halcyon Carrier, complete now with superweapon should vaporize any of the smaller craft almost on contact.
There you go! If this is all too much, then reply and i will build it for you and post it on my filefront account with a name like Super Halcyon Carrier and then just download it and put it in your mod folder. Either way, you now have a SuperCarrier. 
Take care and welcome to Modding!!
-Teal