The American occupation zone of Bremen was the result of Anglo-American wrangling in which the British got northwest Germany as an occupation zone in exchange an outlet to the sea, ie Bremen.

As for Berlin, from an earlier answer of mine

The division of Berlin was a legacy of the wartime Allied agreements over Germany. The wartime Allies envisioned the division of Germany to be an explicitly temporary affair in which the respective Allied powers would denazify the country and end their occupations once an acceptable German government would sign a final, formal peace treaty. As the capital, Berlin had a symbolic and political importance that made leaving it to one Allied power a non-starter. But not very many Allied planners anticipated that the division of the country would last decades when they drew up the occupation zones in 1943-45.

The problem was that the emerging Cold War made a unified Germany a problematic issue. In short, neither the USSR nor the American-led Western powers could stomach a unified German state in the camp of the other superpower. So each superpower nurtured their own German quasi-national governments in their respective occupation zones in the period roughly between 1946 and 1948. So while all the parties, German and non-German, paid lip-service (and some were more serious about it than others) to the ultimate goal of German reunification, the reality was that there were two separate German states by around 1949/1950.

The potential of a united Berlin thus became linked to the wider political settlement of the German question, which meant so long as the Cold War lasted, the city remained locked in political stasis. West Berlin became a de facto part of West Germany, subject to Basic Law and its citizens held FRG passports, but was never an official part of the FRG. The western half of the city also enjoyed a number of special privileges. West Berlin men were not subject to conscription and Bonn doled out subsidies and tax breaks to West Berliners to prevent outflight from the city ( West Berlin wags often termed these breaks Zitterpraemie (jitters premiums). The city's industry also atrophied, and much of West Berlin's economy shifted into the service and governmental sectors.

For the Western Allies and the new FRG government in Bonn, giving up West Berlin would be admitting to the fact of a more permanent German division as well as a surrender to communism. Both the Soviets and the GDR tried various political games of chicken to get the West to abandon the city, and this was why Berlin was one of the flashpoints of the first two decades of the Cold War. The Western Allies recognized that if the balloon went up the situation in West Berlin would have been near hopeless. Most Western war plans focused upon last-stands just in case relief came, but this was not going to happen. Maintaining West Berlin was expensive and not very practical, but it was a political commitment the Allies and Bonn were determined to honor.

Informal agreements with the Soviets in the immediate aftermath of the war allowed for rail and autobahn access for each of the three Allies (US, UK, France) to transverse the Soviet zone to resupply their Berlin contingents. The Soviets and later the GDR honored these agreements in the aftermath of the failed 1948 Berlin blockade and this was how the various Berlin brigades' heavy equipment came into the city. The Western allies were able to get personnel and equipment in a series of scheduled convoys either by road or rail, with heavy equipment favoring the latter mode. The small size of West Berlin placed a natural ceiling on the amount of heavy equipment that could be deployed to the city. The only adequate area for tank training was Grunewald Park and the barracks structures were quite crowded.

This is not to say that military resupply or reinforcing the city was easy for the Berlin Brigades. Both the Soviets and the GDR sought to mire the convoys in red tape and other delays. The Military Duty Trains had to stop when crossing the inner German border and have their locomotives changed out for one by the GDR's Deutsche Reichsbahn, a needless waste of time. They were subject to various searches by the GDR's border police and this posed a problem for shipping new military equipment. When the British deployed their new Chieftain tanks to replace the old Centurions, the British removed top-secret equipment like gunsights, radios, and other sensitive materials before they were loaded on the West Berlin-bound trains. This equipment, along with the tanks' ammunition arrived via an autobahn convoy where the British could keep their eyes on it at all times.

The autobahn convoys were also the sight of various intimidation tactics and other unfriendly niceties to make resupply of the city less than easy. Stars and Stripes has digitized a 1961 account of one such convoy which conveys some of the minutia that typified a convoy. The convoys had to be completely self-sufficient, with the tools to repair any normal breakdown, and could not make any unauthorized detours. One British Berlin Brigade veteran recalled that the drivers for the convoys were all experienced men who were familiar with the route and would not make a wrong turn lest it start a diplomatic incident. The routine nuisances of bureaucracy became much more hostile during times of Cold War crisis, such as the during the erection of the Berlin Wall. David Hackworth's memoirs recalled when his unit was sent in as reinforcements during the erection of the Wall that the Soviet and GDR forces shadowed his convoy creating an apprehension that stopping for a cigarette break could start World War III. But the series of escalating and deescalating crises over Berlin had the advantage of allowing the Berlin Brigades to swap out older equipment for the newer material once their reinforcements left the city.

The long and the short of it is that sending in heavy equipment and reinforcements was not an impromptu affair. The equipment followed a pre-set route and Allied logistics made arrangements with their Soviet and GDR counterparts to ensure such convoys were not a surprise.