Is your 3GB limit the amount of total ram in your system? Keep in mind that you have to leave room for your OS or nothing is going to work well because of all the disk swapping going on.
Your only choice, as far as I know, is to go with a pack based on a Minecraft version older than 1.7.10, which usually ran with a 4GB ram allocation. "Lite" packs were somewhat rare, but they existed and could run with 3GB. You may also have to load an older Java version for compatibility as well.
If you're using 32 bit hardware you won't be able to easily run anything newer anyway, and with version 1.8.x or 1.9.x 64-bit OS and Java became requirements anyway, since a 32-bit system cannot, due to hardware restrictions, support more than 4GB... And yo have too remember that the OS itself uses 25-50% of that.
Every pack since needs more ram until we now have ver. 1.12.2 which needs between 6 and 8GB.