Committing means you lose the $500 deposit if you go elsewhere. Some schools are much more lenient than others about returning the money if you ask (nicely), but I don’t know what UChicago’s stance is. If you end up getting into another school, with a better aid package, then you can go elsewhere.
Committing now shouldn’t affect need-based aid, which is divorced from admissions (and therefore the day-to-day business of maximizing yield). The only way the aid office will know to be extremely concerned you’ll go elsewhere is if you tell them. For instance, letting them know about a very different aid offer from a peer institution.*
*There is a right way to do this, and a wrong way. To keep this short, I won’t delve into the details, but it’s not a move to make before asking around here on CC. Even some GCs know surprisingly little on the matter.
If you’re expecting a change in family circumstances, you can let the aid office know right away, detailing the impact on your finances, and politely ask them to reconsider their offer. Do not say that money is all that’s keeping you from attending - the aid office has formulas to determine need, and if the University believes it’s your first choice, they’ll offer a package they “know” you can just barely afford. Unless you have a vastly superior offer from a peer school (see above), they assume most students would walk over a bed of hot coals to attend, and will take the borderline affordable aid package. However, if a student’s financial circumstances change a lot - one parent losing her job certainly counts - the U of C has no incentive to make someone’s net price unaffordable and bring the University’s yield down.
The one type of aid that will be affected if you enroll is merit aid. UChicago (and other schools with merit money) use it to boost yield, making offers to applicants who might otherwise go elsewhere. I waited until March to commit, despite getting in EA, on the chance I’d get some merit money, which is exactly what happened (Cambridge for $13K/year wasn’t a bad backup option either). I assume I set off a red flag in their system, or in my regional counselor’s head, and the U of C offered significant merit dollars. You’ll notice this trend if you pay attention - a lot of University Scholars are people who waited a while to commit, or URM applicants with a strong profile (likely to have some very good options after Ivy Day). Everything I’ve seen during the RD round confirms this: merit aid has become yield-maximizing aid, and by committing you lose a lot of leverage - it signals UChicago is your clear first choice.
Given the above, only you know what’s best for your own situation, but hopefully this wall of text is some use to you and your family.