End of the war the Germans had around 328,000 personnel in Norwayicon, of which 53,000 had retreated out of Russiaicon/Finlandicon and were still in contact with the Russian northerner front (sort of)

Norway was an integral part of the German war effort. Most of the aluminum ore was processed in Norway due to the hydro-electric capacity, and Norway was required for iron ore shipments from Sweden in winter (via Narvik)

Lastly in the critical days of summer/fall 1942, when the Germans were attempted to beat the Russians before the second front was established, Norway was the main base for attacking allied convoys:

PQ15 lost 3 convoy ships out of 25, plus two escorts
PQ16 lost 8 convoy ships out of 25, no escorts lost
PQ17 lost 24 out of 34 convoy ships
PQ18 lost 13 out of 40 convoy ships

The amount of material lost in these convoys was quite large.

In any case the Germans had to invade, the UKicon was planning to do it a few days after the Germans struck, as if they took Narvik the Swedishicon iron ore supply would be halted, which Germanyicon could not permit and keep war production going. Forget the percentage of total German production but it was in the 20+% (or more).