I don't use Tacky Boxes but polycarbonate & silicone are heavier than aluminum & plain foam...
In regards to foam or silicone, I may be in the minority here but I really don't like any kind of slotted whatever because I find it too fussy, I can jab WAY more flies of various sizes in plain flat foam AND I can orient them the way I want.
I can't explain why but for me, it is way easier to remove or replace a fly from a foam sheet when the flies are oriented horizontally versus vertically, especially at the top or bottom of the sheet. Because of this, all of my fly boxes with foam are set up this way.
I realize I could just turn a slotted flat foam box 90 degrees but the lid may need to be held up or depending on the box, the slots are oriented the opposite way from my preference (insert to the right, release to the left). In addition, unless I'm doing the minimalist thing, I'm using a Richardson Box which can't easily be turned 90 degrees.
Other issues with slotted foam: I fish really small stuff and trying to get sub size 26 flies into any foam slot is beyond the capabilities of my fat fingers. I also can get double the amount of flies in a plain flat foam sheet versus a slotted sheet (I know because I counted). That means less space/fly boxes required.
When I first bought my current Richardson Box almost 20 years ago, I opted for the flat felt pads to use in a non compartmentalized tray for nymph/wet fly storage. Those felt pads were garbage so I made my own foam versions by gluing two sheets of Walmart craft foam together.
Even though they have battle scars, the homemade Walmart foam pads are still going strong even though I made spares just in case. With my factory flat foam boxes, I bough a few spare pads but to be honest, unless you are hung up with pristine foam, I really haven't found a need to replace any foam in any of the boxes I own.
The least expensive option in your case would be to pull out the silicone Tacky Box inserts which is probably most of the weight. You can save & reuse them or I'm sure even sell sell them to recoup some of your investment and replace them with plain flat or slotted foam sheets.
Try it on one box first and see how it goes and if it represents a decent weigh reduction, do the rest.
Good luck!