I've hauled many heavy things in my A Pickups, most loads of which were over 1/4 ton.
The '31 with a new rear spring, loaded down with 2 complete FE series 390 Ford engines and a 4spd trans the truck was just barely squatting in the ***(maybe 2 inches). I figured the load weighed 1500 lbs counting the small parts, engines and a cast iron case 4spd.
Another load was a pile of scrap going to junkyard-load was a tad shy of 1200 lbs according to the scalehouse ticket, here again no problems.
I had no problem stopping nor did I suffer any ill handling effects. Weak springs will most certainly affect your hauling capabilities not to mention handling. Most "restored" A's I see still use worn out original springs.