Britain carried out several commando raids on Norway and there was a strong resistance movement in Norway. Between them these convinced the germans that if they didn't have a significant force in Norway sooner or later they would be driven out. A D-day type invasion of Norway was always possible, and if Germany only had 50,000 troops there, it would be probable. The ability for Britain to severely cut Germanys steel production was just too tempting, and once the Germans had Invaded Norway there wasn't the political problems of Invading a neutral nation.
Edit; I just don't think it would have been viable for the Germans to Keep security over their Supply lines and Critical infrastructure with a small force. They would have been to vulnerable to attacks by resistance and commando forces.
Then we're still back to "How much is Norway worth versus the garrison requirements?"
If 50,000 is too small, then 100,000 would be better and still not as costly as 300,000.
Keep in mind that I don't think Norway makes that great of an invasion target AND I don't think garrisoning the whole country is necessary to secure the iron.
Of course, any Operation Overlord style invasion could probably succeed. But, now we're playing the "How much did the Allies spend cutting Germany's supply of iron through Navik, and how much time did it take?" game (with some lovely prizes for the winner, I might add). If 100,000 troops tie down the Allies in Norway for 3 months, that's 3 months + who knows how many more not spent invading the industrial heartland of the Reich while the Soviets are either advancing towards Berlin (Operation Bagration) or fighting for their lives at Stalingrad (or even worse if its earlier).
The opportunity costs might be significant for both sides. At a certain point, Germany pays more to garrison it than it's worth, and at a certain point, the Allies spend more than the opportunity cost in time and manpower than it's worth to cut the resources.