pcpunk, that's a Sandy Bridge CPU in there, among the most coveted today, there's still many whom won't give up their soldered IHS on die for (roughly) 10% more raw power. Plus no need to be concerned about a future delid, which most all Ivy Bridge & future gen models will need at some point, it's not a matter of if, rather when the procedure will become needed. Due to more heat, likely sooner on notebooks as a whole. That's why I clean & dust often, no less than once yearly on notebooks, to include a fresh application of thermal paste. Because you have a better manufactured CPU than those of today on the Intel side, you can clean w/out reapplying thermal paste every time. maybe every two years.
Plus can be upgraded to an i5 or i7, that is, if you can afford inflated pricing on eBay. If there's any computer you have with a SSD installed & want it in the best model, this is it!
Max out the RAM at 8GB & be done with it (& hopefully the CPU later), you're on the way to some high powered 64 bit computing.
Check out the volatile pricing for your CPU in this year alone, has broken the $175 mark three times this year (likely eBay/Amazon pricing), probably more than when new!
Chances were, the 32 bit OS was installed for a specific reason (custom order), maybe the original owner(s) needed it when moving forward from XP Pro, and there were no 64 bit equivalent software choices to meet the need (why Windows XP Mode was offered to Windows 7 Pro, Ultimate & Enterprise users). You really have two OS's in one if needed & this still remains available today, however I'd not want XP Mode nearing the close of 2017, although until SP1 was released in 2011, did use for important things, like filing tax returns. That was when the old rule of waiting until the first SP shipped before considering the OS as 'ready for serious use'. To some extent, this remains the case today, on Day One of the W10 Fall Creator's Update, many had issues with the Start Menu not working right, I had two to do so, one was AMD, the other Intel, so the only one to point the finger at was Microsoft, it was their upgrade. Oddly, on the AMD PC, had been running the Previews for months with only one small issue, this has left a very bad taste in my mouth towards W10. I'd not advise you to give the a shot, even if you can, unless after first imaging of the drive for a fast rollback, take the leap & sign into your Microsoft Account (Outlook or Hotmail), and then image again.
This would preserve future rights to later apply the backup image & upgrade to the latest version, if desired.
To a much lesser extent, the need for 32 bit OS's are still the case today, W2K still powers a lot a diesel rebuilding operations (machinery), why would a profitable business dispose of tens of millions of dollars of equipment over a $200 OS? While the main office are likely powered by modern computers, there's still lots of equipment in factories powered & monitored (offline) with 32 bit OS's, a few of which may require 16 bit software, which is impossible on a 64 bit OS.
Back to your OS, no need to worry, Windows 7 still have a solid lead over Windows 10 at this time, oddly around this same time in the life of Windows 7 (SP1), usage had long surpassed that of XP & Microsoft then started with the warnings of staying on XP as being 'dangerous'. This shows that many stood behind their 'No' when Microsoft tried every possible way to sneak it (W10) in & may continue to well beyond EOL in 2020. It could be that unofficial EOL for both W7 & 8.1 will happen at the same time in early 2023, because like XP, it's going to be hard for 3rd party offerings to turn away even as little as 25% user share away.
Furthermore, I don't see any issue with clean installing the 64 bit OS with your media, provided the ei.cfg file is removed & you select Windows 7 Pro & use the proper COA at time of install. Not only does it unlock all versions from the Retail media (Starter to Ultimate), also OEM, System Refurbisher, Upgrade. Many field technicians has carried this around for years, there was also a pre-SP1 version of the media, as well as a combined 32 & 64 bit ISO (requires more work for the Home user to create). This saves time, to have all possible versions (other than Enterprise) on one DVD and USB Flash drive, where time equals cash, for every 10 minutes saved on a job, that'll allow to get another in before the end of day.
At any rate, you now have a contender notebook, provided it's in good shape. Before you get rid of the current OS, please be sure to image the current install first, or remove & save the current drive (use another) until you're sure that the 64 bit install is installed, activated, updated & imaged. Some apps may also require validation of OS, although haven't seen this in quite some time. Also, if you wish to use a SSD, better a clean install than a clone later, which normally should setup the drive & registry keys as should be. If cloning, these settings needs to be manually performed, or performance, as well as active TRIM & Active Garbage Collection won't do it's job as intended. Why most who prefers SSD's goes with a clean install and then images as soon as updated. Although before any 3rd party software installed, such a CCleaner, Speccy, etc, (this provides for a 'fresh install' when needed) & in the case of this notebook, looks to be the best posted that you currently own.
Take care of it & should meet your needs for years to come, even more so when the Sandy Bridge mobile i5/i7's drops in price.