It will not weaken the brass any, but it does work harden the brass. No more so than using a non bushing full length sizing die with an expander and certainly less when you measure it very finely as described by
@Lunchbox27 above.
It does work harden the brass more than using the precisely chosen bushing to get exact neck tension you want, but again as noted above, any variation in neck wall thickness is pushed to the inside and can add to lack of concentricity. If you're turning necks and using bushings, you are adding a step that work hardens the brass more and doesn't provide any concentricity or accuracy benefit.
Even if you don't turn necks, I've measured neck thickness variation and haven't come across any lots where the average variation exceeds 0.001" and the maximum variation more than 0.0015". I've only done that with premium brand brass, though. If your concentricity is less than that, you're doing OK. My concentricity is acceptable on the neck but when I measure halfway between the ogive and tip, I have some issues. The location pretty much narrowed the issue to the seating.
Full disclaimer, I don't turn necks and I do use a bushing then open it to the exact size using a mandrel. I bought several sizes of 21st Century mandrels so I have the expander ball that came with the die, plus four smaller mandrels in 0.0005" increments. In my .338LM I found that 0.003" interference fit gave the best accuracy across the powder charge range and particularly at the optimum charge. It was a measurable difference.
If you're only hunting and want sub MOA accuracy, that's fine. If you're only hunting woods and fields where your maximum shot will be 200 yards, even that might be overkill. If there is no practical limit on how far out the game might present itself, the difference between .6 MOA and .8 MOA just extended your reach by enough to offer more good shots provided you know your dope and can read the wind.
You get to decide how far down the rabbit hole you want to go unless you are just unable to control any inherant OCD traits. This is just a matter of the degree to which you are analytical. There is a shorter descriptive that applies to those unfortunate enough to be so afflicted.
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