The question whether or not the German conquest of Norway was strategically beneficial to German aims is often misunderstood. The benefits to Germany were largely three fold, and it is these three reasons that often blind people when evaluating the strategic implications of the invasion.
Firstly, the securing or iron-ore from northern Sweden was an obvious gain, as was the acquisition of Norwegian docks and fjords to base German surface warships and u-boats. Thirdly, with the Germans planning on attacking the Soviet Union, any future convoy (material) assistance by the British to the Soviets would face the prospect of a costly naval route patrolled by German warships.
However, the far less obvious results of the invasion ultimately highlighted why the German invasion was a strategic blunder.
The immediate cost of the invasion was the loss of almost 6000 troops and 200 aircraft. Added to this was 3 cruisers, 10 destroyers and 6 submarines, plus a further 3 cruisers and 2 Battleships out of service for periods up to 12 months. With the losses the Germans would suffer in other campaigns, the losses in Norway may seem fairly un-important, but as pointed out earlier, it was the less obvious implications that would cost the Germans so dearly.
Firstly, Norway would require garrisoning, up to the end of the war in 1945. For the duration of the conflict, 12 Divisions were tied up in Norway, even though they never saw serious action.
Secondly, by attacking a neutral country, Hitler further antagonised other neutral powers such as the US. Furthermore, with the conquest of Denmark occurring alongside that of Norway, the British were free to take over Iceland and Greenland, which provided the allies with key air bases to defend the convoys in the North Atlantic.
Thirdly, and most importantly, the Norwegian campaign was a disaster of sorts for the Kriegsmarine as it lost 16 months in its prosecution of tonnage warfare. In 1939 Norway possessed the 4th largest merchant navy in the world. With the German invasion and conquest of Norway, 4,600,000 tons of Norwegian shipping sailed into British ports. Sinking of allied shipping by u-boats did not exceed this figure until December 1941.
So for the acquisition and securing of iron-ore from Northern Sweden the Kriegsmarine lost 16 months prosecution of tonnage warfare. The acquisition of docks whereby u-boats could operate from was fairly unimportant when France surrendered only a few months later, providing the Germans with bases along the Atlantic coast. The German presence in Norwegian waters to disrupt shipping to Russia was again, fairly un-important. Especially when you consider at this time, the Germans had little faith that the Soviets would survive their initial attack. Once Britain and the Soviet Union allied, material loans by the British and US had little real significance on the Eastern front, and in any case, those shipments, which had an impact, did so because they made it into Russian ports. Therefore, the German invasion of Norway was a strategic error. Hitler wished to act strong, but by doing so he served up a disaster for the Kriegsmarine.
H.P.Willmott. The Great Crusade.