The question isn't expanding on what kind of paywall / paid tier we are talking about, so I will try to discuss various options. I will try to be as objective as possible to avoid putting my feeling as one of the reason this is probably a bad idea.
First option: Hide the content behind a paywall
I am not even sure this is actually possible given that all the content so far has been covered by the Creative Common license - I am not sure it actually allows you to ask for a payment on the content.
What really matter anyway is that it certainly allows for redistribution of the content with basically just the need for attribution. Which means that as soon as Stack would try to hide the content I posted behind some payment requirement... I would be probably allowed to repast the content I posted on another, free host and attribute it to myself. If I felt particularly "evil" I could even build a free browser extension that given a StackExchange question url gives me the equivalent GitHub hosted replica.
I would hereby conclude that this is not possible.
Second option: buyable privileges
It doesn't matter if we are talking about buying rep coins, paying for bounties, unlocking privileges with money or anything else. The second you add "microtransactions" to the SE "game" you are creating two kinds of users: the ones who pay and the ones who don't.
And it gets better from there... yep, because obviously the ones who pay would probably want to actually get some advantage over the ones who don't... And now they are actual paying customers too...
Bought rep? Well, it will be nice to see what happens the first time a paying customer laments that "Mr. Evildoer downvoted him without reason" and some user tell him to "grow up" because "downvoting just means Tim lost his keys again". Maybe so far we were fine with the idea that voting wasn't really that much regulated and no one would need to explain anything - you could even downvote because you didn't like the poster avatar... Now, tell that to the guy that just lost MONEY because you negated his bought rep points. Maybe our voting rules work when there is no money involved, but I am not that sure they would work afterwards.
You bought actual privileges? Great, now you have a customer that have powers than aren't tied to actual merit. Can he close question? He just can edit existing ones? Does his decision to close a question have the same weight of a mere "free tier guest user" (I am starting to think Roblox here...)?
The idea behind reputation was to measure the "trust" you gained, with more "powers" give out the more trusted by the community you are. That way, we "delegate" the more sensible work to the users that have shown to be more trustworthy...
It is pretty evident that the instant you add "buyable TRUST©" to the equation... all falls apart.
Third option: buyable usability
You could try and have users pay in order to get a more user-friendly experience on the site. After all, we already do this: you buy the "reduced ads privilege" with your work on the network. Problem is that users are probably far more inclined to pay with posting answers than they are with actual money.
Pay to remove ads? Well, you are a web site, not an "modifiable" android app... Ads blocker exist for a reason, and I don't think that a race-to-armaments attempt at discouraging ads blocker is a battle SE can hope to win.
Find other usability features to sell to willing users? Again, I don't think it will work. Over the course of the years, a lot of users have already filled holes for features that have historically been ignored: canned comment support, custom alerts ... if you need it, probably there is an user script available.
In this case, it seems that there is actually no market available for this.
Now this may work.. but I don't actually see what extras could be provided. Autographed Skeet photos? All year round hats? It really depends on what would be offered.
I don't think the network is in the position to try to add buyable content now, but I may be wrong. What I am pretty sure of is that even if you manage to find some way to have buyable stuff that does not get in the way of the normal site usage... you will have to be very wary of the way the "extra" are actually perceived. Far too often the "extras" I see in games and apps seems more like "minuses" for the ones that aren't willing to pay an extra $$$ for the day-one paid DLC of already-on-disk content.