1. Public charge inadmissibility and deportability grounds.
The INA 212(a)(4) public charge ground of inadmissibility applies at the time of your AOS application, not now that you're already a permanent resident. Receipt of public benefits will have no effect on your I-751 or your naturalization.
A corresponding ground of deportability exists, INA 237(a)(5), but is almost never charged and, if ICE hypothetically tried to charge you with it, you would win because you "became a public charge" from causes arising after entry. (Plus, you only become a "public charge" if you get cash assistance. Food stamps don't make you a public charge.)
2. Eligibility for public benefits.
A permanent resident is eligible to receive public benefits if they became a permanent residents more than 5 years ago (but a select few of them don't have to wait 5 years). See 8 USC 1641(b)(1) and 8 USC 1613(a). This means that you might not eligible for welfare, but your citizen spouse and child still are. Your status will have no effect on their eligibility for benefits.