Very interesting that you would be willing to make yourself into yet an even weaker entity. What a tragic and utterly preventable denouement for a once proud empire.
I'm curious in what way you think rump-UK would be weaker without Scotland? Economically it would be fine: England is by far the biggest economy in the UK. There would be some losses: about 10 percent of the UK GDP, Scottish military bases, natural gas and oil resources, about 5 million people.
But Scotland produces only about 6 percent of the UK's total exports. The vast majority of what it produces is "exported" to England, Wales, and Northern Ireland (about £50 billion to the UK compared to £15 billion to the EU and £17 billion to the rest of the world). It also has a fiscal deficit that's largely offset by the English taxpayer. Scotland is much more economically dependent on the UK than the UK is on Scotland.
Outside of the UK, Scotland may be a credible middle-ranking small country comparable to Czechia. It certainly could not afford to maintain its current level of public services. Without Scotland, the rest of the UK would remain one of the largest economies in the world.
(btw, Scotland was never an Imperial possession of British Empire. The Union with Scotland was peaceful, and largely in the interests of the Scots, who had succeeded in destroying their economy through mismanagement, unwise allegiances with the French, and unsuccessful attempts to build their own empire).
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.