Figured out how to do it…
For posterity, I will explain (possibly to my future self next time I have this question, too):
1. Create weight-based shipping classes based on poundage. Put the charge in the Handling fee and leave the per pound charge blank or 0.
For example, 0-5 lbs = $4.99 Handling Fee with a Minimum weight of .01 and a Max weight of 5 lbs.
5-10 lbs = $8.99 Handling Fee with a Min weight of 5.001 and a Max weight of 10 lbs.
Etc.
2. At some point, you have to stop with the weight classes because you can’t make weight classes to infinity. So, let’s say your final class is 20 lbs and over… You might set the Handling Fee to $16.99 and then an additional per-pound charge of $1.96/pound. Your Min weight would be 20 and you leave Max weight blank. Now they can keep adding items to their order and the shipping will automatically be calculated to infinity. Admittedly, this could get ridiculous (not sure) if someone orders 100 lbs of product (I think using our example, that would be a base charge of $16.99 for the first 20 pounds and then $160 for the next 80lbs. Surely USPS has better rates than that, but you can adjust accordingly once you go to USPS and figure it out. I haven’t bothered).
3. The final thing is to just select “Automatic” from the Shipping main area for the “default shipping” option. I don’t know how necessary this really is with weight-based shipping if there are no other options like Free or Flat Rate or whatever, but I don’t see a reason one of the Weight-Based shipping classes should be default. I suppose the lowest class of 0-5 lbs at $4.99 would also make a good default option.
