Low level cars have 4 leaf packs. The performance cars came with 5 on the left and and 5 with 2 half leaves on the right. If someone put competition springs under yours, it could have even more. If someone modified your original set, you could have a single, thicker leaf in there as well.
Yes, some leaf packs are fairly stiff. However, some shocks are similarly stiff. To differentiate, you can disconnect your shocks and see if you can now move the suspension. If yes, you have a shock problem. If no, then your spring pack is the issue.
You do want a fair amount of clearance between the housing and the bumpers so you don't bottom out, but you don't want them too close either.