Will heavy tires make a difference for climbing? I have a pair of conti 4 seasons and a pair of marathon pluses. I use the latter on a daily basis for commuting because of their puncture resistance, and haven't used the contis in a while now. I will be going on a tour with quite a lot of hills and climbing. I will be taking a couple of kg of stuff in a rucksack. The question is, will there be a noticeable difference between using the marathons vs using the contis? Will the rolling resistance make any real difference (for climbing)?
There is no way tires are different than other weight when climbing. The saying about rotating mass being equivalent to double non-rotating mass applies only when accelerating and even then you have to take into account that tires are quite lightweight compared to rest of bike and rider.

Rolling resistance difference can be noticeable even when climbing, but Conti 4 seasons are among the worst road tires and Schwalbe Marathon plus is one of the best rolling extremely protected tires, so the difference isn't necessarily that great.