The 3.5 tons refer to the GVWR of the vehicle, not the actual weight (presuming you are not overloaded).
With your camper loaded, you sure are at 5+ tons actual weight. What is the GVWR of the truck? 14k?
They do not normally weigh you in most countries, with the exception of Austria maybe. Even they may shy away from the bureaucratic hassle in your case, but I would not count on it.
But it is getting more common.
The general height of all underpasses is at least 4.0 meters, if they are lower, they will have signage up. It is up to you how soon you notice. And some of these are in places where you can not turn the truck around and you may have to backtrack a bit.
The maximum allowable vehicle width in Europe for a normal vehicle is 2.55m - you are close to that, possibly over when you measure from the outer edges of your jack bases. It can be challenging. Rural roads are often very narrow, one lane. In some places walled in with stone walls. In most others, there are ditches or soft shoulders, so you need to be very careful. You will sometimes wish you had taken off your jacks.Main roads will never be an issue. If a heavy truck can get there, so can you.
You need to be aware that a duallie will not be fun in some places due to the wide rear track and the overall size, and that you may have to compromise on the roads you take (truck route vs. back country). Be prepared to occupy four spaces in the parking lot of the supermarket ;-)
Eta: and nowadays many parking lots have height restrictions (as in physical bars over the entrance) of varying height, to either deter overnighting truck drivers or traveling folk. But even a rented euro camper will be too high for those.
