I have cyclocross bike with alu frame (Focus Mares). It is currently running on Continental Cross tires which are around 400g. I mostly ride it in city and sometimes go for weekend tours in countryside, but also on solid roads. Now I thinking on putting Schwable Marathon Plus 37-622 tires on it which are around 960g. Is it fine to do that? I get more robust tires, but at the same time solid weight increase. Will it make any bad impact on frame reducing its lifetime for ex.?
No, mounting different tyres will not affect the frame or bike lifetime.
Schwalbe Marathon Plus are very common tyres on this type of bike. Focus sells the commuter version of the Mares AX even with such tyres (Conti Touring Plus).
However you will experience a different ride. For instance grip, comfort, and rolling resistance suffer a little with tyres with such good puncture protection. The weight is only a minor factor. Reduced suppleness due to the protection layers is the main reason for this.
Still, Marathon Plus are excellent tyres and will serve you very well for the described use cases. For equal puncture protection and a faster ride you would have to pay twice as much. For good roads you might consider a good all-round road tyre in 28-622.