This is obviously a massive question. Really, it's multiple questions rolled together - how did Nazi Germany justify its behavior during the war? How did it maintain public support over time? To what extent was it success at doing so? Was there significant war-weariness at home in wartime Germany? These questions have very different and at times wholly unrelated answers.

I can give you a few thoughts:

1. Aggression is a slippery idea. German propaganda was adept at portraying aggression as either a justified response to outside provocation or a good thing in itself. (For the latter, see Klemperer's discussion in The Language of the Third Reich of the normalization and glorification of concepts like aggression, violence, and fanaticism in the Third Reich.) Germany, according to the common Nazi narrative, was beset on both sides by enemies conspiring to see its downfall. There was a fair amount of anti-semitism, as well as revanchism/expansionism mixed into this narrative: the Jews were often portrayed as being behind the cabal of enemies, and it was taken as a matter of course that Germany's re-acquisition of previously German territory and initial acquisition of broader Lebensraum in the east was legitimate. Later, of course, there was no need to justify new aggression at all: The defensive war of 1943-45 was portrayed as a last-ditch "total war" in defense of European civilization against the encroachment of savage, asiatic Bolshevism. Generally, the Nazi government and German culture gave their people every conceptual element necessary to justify barbaric military aggression.

2. War-weariness was real in Nazi Germany, though it took some time to become widespread. The war didn't really "come home" to Germany until much later than you might imagine. Mass casualties at the front weren't a thing until the debacle outside of Moscow in December 1941. The Allied strategic bombing campaign didn't pick up steam until the summer of 1943. The German economy was not fully on a war footing even after the declaration of "total war" in February 1943. There was, however, growing discontent and fear among the German people as the war progressed. Shortages became more acute, casualties increased, the war effort claimed more and more of the economy (making consumer goods more expensive or unattainable), the bombing became more intense. As the front collapsed in on the Reich, defeatism became widespread. Surveillance reports from the SS Sicherheitsdienst indicated that by late 1944 public confidence in the government was eroding all over Germany. Even among patriotic Germans who dutifully feared the Allied advance, hoped for deliverance through the so-called Wunderwaffen, and were worried about revenge for German mistreatment of Jews and other civilians in occupied territories, a sense of gloom was pervasive.

3. The extent to which the war did not break the Nazi grip on power until the bitter end is tragically remarkable. Ian Kershaw's book The End makes this point: Total conquest of a major power, to the point of occupation and dismantling and rebuilding of its government, is a rare thing. Usually, before that point is reached, the losing power either sues for peace or is overthrown from within (the examples of Imperial Germany and Imperial Russia in 1917-18 are instructive). In the case of Nazi Germany, the NSDAP managed to hold onto power until it was finally and totally destroyed. No serious terms were offered to the Allies, and no widespread movement of resistance stood up to Nazi authority. This is a difficult historical phenomenon to explain, because that involves explaining a wide array of public attitudes in Germany toward the war and the Nazi government. Doubtless fear played a role, as did coercion - tens of thousands of German soldiers and civilians were executed by the government during the war - but so did sincere belief in the Führer, Nazi ideology, and the Endsieg. That sincere belief maintained wide currency long after the war was effectively lost. There were also structural barriers to resistance: the dominance of the Party in setting policy and the neutering of the military resistance left little conceptual space for political rebellion in the last months of the war. Fanatics were setting the agenda up to the very end.