Tire weights come off time to time. Since tires were removed could of happened. Tires could wear different depending on location and if rotated could cause a vibration at a different location. Lots of reasons to get a vibration jitters seems to be tires not suspension.
One could have separated. It happens a lot.
Sure, and meteor could fall on you while working on the truck also. But seriously, there is a chance either of those happened. But if the truck runs fine when you pull it into the garage and then as soon as you pull it out of the garage the issue occurs, it would be a pretty big coincidence. Sure, it's not that uncommon for a tire to separate but it also doesn't happen with a high frequency nowadays....and the simple act of removing a tire in the garage and putting it back on shouldn't cause it to separate. In regards to tire weights, again there is a chance a tire weight got knocked off during the work but it just doesn't happen that often. I've had the tires on and off of multiple vehicles hundreds of times over the years and have never knocked a weight off....again, yes it can happen but it's not like a regular occurrence everytime you pull the tires. Also, just one wheel weight being knocked off doesn't necessarily cause a noticable vibration. Just about any tire and wheel assembly will "change" balance as it wears...that is why people will often rebalance the same tires and wheels periodically. I've rebalanced several sets of tires over the years and found them to be way off from the original balance, and I was doing this just for maintenance reasons and not because there was excessive vibration.
So yes, either of those tire related items could possibly be an issue. But my main point is those issues are not super common, there is no reason that a tire would separate by unbolting it from the truck and bolting it back on, and even chucking a wheel weight does not necessarily cause that big of an issue.
Of course in the end, and as I mentioned before, it's really hard to diagnose the issue over the internet. A tire related issue like separating belts provides some very specific vibrations and noises, and you simply don't know enough details over the internet to diagnose if it's the right issue or not. I just went back and re-read the OP and based on that description tires are one of the last things I would look at. They mention worse ride characteristics and that it is okay on a perfectly smooth road. Well, a bad tire would likely be more noticeable the smoother the road is, and that is because it's not being masked by bumps in the road. In general there is a big difference between overall ride quality and a constant "thump, thump, thump" and shaking of a bad tire that also would increase with vehicle speed.