Setting Weight for Lot-Based Product Listings

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Hi there, I've tried to find a post that will provide a solution to my particular issue, but have yet to find one.

My issue:

As an example, I have some fossil jars w/lids in my shop. I have a total of 18 jars and buyers have the option of just choosing how many of the jars they want, not which specific jar they'd like.

Buyers instead will get a random jar when they purchase as they are all relatively the same in size and style (although they vary in natural fossil formations). However, it is reasonable to assume that some jars will be differ in exact weight from one another by anywhere from 5-18 grams.

For example, I weighed one jar from the lot and it is 258g, one was 250g, and another one was 242g. I can reasonably assume all of the jars won't weigh exactly the same, although they will be within a close range of one another.

If a buyer is gong to randomly receive a jar from this listing, how do I set up weight for this listing so that shipping cost is calculated for the custom upon purchasing? I have other items that present the same issue (a listing for quartz points, a listing for palo santo sticks, listings for 4" smudge sticks of various kinds, etc).

It's easy to set variant weights for product listings where each item in the listing will be shown and can be individually selected in the variant drop-down list above "quantity" but again some of my products, like aforementioned, are lots that buyers will randomly get a selection from. 

I'd appreciate any help in remedying this issue so that I can list and assess my items properly in the shop before I launch my website and make it public.