There are very good technical reasons for moving to 64-bit applications, mainly to do with performance improvement in processing and an access to hardware features in the chipset. Add into it that many of the tools used in the client are, I suspect, now targeting and not supporting 32-bit deployments, then this is an inevitable move if Eve is to have a future.
Long technical here in the forum.
If you are running on a PC that meets the current minimum supported requirement then you can run a 64-bit client (and probably already are).
Firstly, that AMD x2 chip is a 64 bit chip.
If you are running any Microsoft operating system after Windows XP then it should be running in 64-bit mode (only the professional version of XP supported 64-bit hardware).
If you are running XP please, for the sake of the rest of us get off the internet - old, unsupported insecure nonsense like that is what is exploited by DDoS networks to the misery of others (I don’t give a damn about loss of your data/bank details/credentials - that’s your choice, but you being a threat to others isn’t really acceptable behaviour).
I’d also recommend getting off Windows 7, it’s not completely compromised, but it’s unsupported and down hill from here!
If you need a newer, supported OS, then various Linuxes (Linii?) are free and will run on your hardware. Eve runs fine under Wine - many guides are available. Heck, that’s how I run it.
I’d even suggest Windows 10.
Anyway, unless you’ve expressly rejected the 64-bit client; or it hasn’t deployed onto the archaic OS you’ve chosen to run then you’re already running a 64-bit client.
If you look in the task manager it may well tell if it is a 32-bit or 64-bit version that is running - you are looking for the client, not the launcher - The launcher is 32-bit and hasn’t been changed (it really doesn’t need the performance boost given what it does!)
Eve Client isn’t suddenly going to jump to demanding more memory at the end of the month, as CCP Caffeine said. But it will increase over time, because Eve will move forward - even if you can’t.
In terms of client demand Eve isn’t overly demanding on any vaguely recent system.
Your problems are fixable, even assuming actually have a problem.
But seriously, newer (not even the latest) hardware will give you a much better experience - you may even find that Eve isn’t the jerky potato game you are probably playing at the moment. And a second hand system will be fine - re-use the screen, keyboard and mouse to keep the cost down.