I fought a weak battery problem for over a year. Off and on problems starting, even in nice weather. I even had to pack jumper cables cause I never knew when it would strike. I finally bought a hYTX20DHL battery from BatteryStuff.com for $99, including shipping . I have not had a problem with it starting, even in the 30' weather we have had here. I am impressed!!! to say the least. They make a regular model of this battery for the RIII and they make the same battery for the HD, I thought if they make one that will start a Harley it ought to be perfect for me and I bought it. The description is 'YTX20HDL 12V HVT-1 HD AGM Battery Powersport.
Try it, you will like!!!!!
Bob