Your own first paragraph demonstrates the answer to your own question. 10% GDP is loads, and some of those military bases are the only places you currently have where you can fix up your “independent” nuclear deterrent.
Yes, the GDP reduction isn't trivial, but Scotland spends way more than it makes. The UK would no longer have to support that deficit and they wouldn't have to provide services to 5 million Scottish people.
The loss of the HMNB Clyde (the Trident base) poses problems, but not insurmountable ones. Devonport in Plymouth and Miford Haven (more problematically) are suitable replacements. Also, Trident provides about 8,000 jobs to the Scottish economy, and they'd all move south too.
You are asking why the UK would be weaker without Scotland. I do not understand why you do not find convincing the very claims you already concede? 10% weaker is weaker, specifically by 10%.
I do not find it convincing because reduced GDP does not equate to weakness. It has to be viewed in context: GDP would be reduced but per capita GDP would not be reduced by 10 percent (because the population would also be lower). Furthermore, the UK spends more on Scotland than Scotland contributes, so it's a net economic burden. Independence would remove that burden, leaving the UK better off.
I think I have already expressed this perfectly clearly in previous comments, so this is the last I will say about it.
Is West Germany better off with East Germany or without? Or how about is California better off with Alabama or without?
By all means continue to shrink yourself down into the smallest tribal sub-population you can slice yourself into. I’m sure prosperity is right around the corner when you finally do.
The loss of the HMNB Clyde (the Trident base) poses problems, but not insurmountable ones. Devonport in Plymouth and Miford Haven (more problematically) are suitable replacements. Also, Trident provides about 8,000 jobs to the Scottish economy, and they'd all move south too.