There is important context in that about 4 out of 5 of all Wehrmacht soldiers killed died on the Eastern Front, which is somewhat remarkable when you consider how many US, British and British Empire forces were mobilised and participated in the European war. Of course, the US & British (inclusive of empire) did a lot of heavy lifting in other ways (production, supply, naval and air wars, code-breaking, etc), but it's nonetheless useful to understand the Soviet perspective.

Regarding the question, it does not seem the Western Allies wished to see the Soviet Union and Nazi Germany bleed each other dry. Stalin often repeated this line as justification for the Molotov-Ribbentrop Act and generally considered - like many other leaders before him - that he had the measure of Hitler in the agreement to carve up Eastern Europe. There are some *alleged* letters sent from Stalin to Hitler during the months before Operation Barbarossa indicating this understanding, and some historians have claimed that Stalin was so shocked by the attack that he had something of a mental breakdown and effectively briefly went into hiding after the disaster of the German invasion unfolded. When the German troops were amassing on the Soviet borders, there was intelligence shared by the Allies to Stalin that indicated the attack was coming. During this period, Stalin was quite convinced that the Allies were trying to instigate a conflict between Germany and the Soviet Union to bleed the two countries. He did not want to provoke Germany unnecessarily and, as we know, the Soviet forces were caught out very badly when the assault began.

As the war progressed, the UK was desperate for the Soviet Union to hang in and publicly its leadership spoke of its support for the Soviets. When Churchill was asked about how he could speak in support of the Communist dictator, he retorted "If Hitler invaded hell I would make at least a favorable reference to the devil in the House of Commons."

After the US entered the war and communications and summits between the "Big Three" began to grow, Stalin was forceful in insisting that the Western Allies opened up a second front in Europe. He was particularly frustrated in November 1942 when the US entered the fighting in a big way through the invasion of North Africa. However, this decision to target North Africa was largely due to the determination of the US to get its soldiers fighting and due to the limitations of shipping. Even this operation in North Africa cost a lot in terms of global supply because merchant shipping and naval escorts were a significant limitation on the conduct of the war for the Allies, and this size of operation was all that was manageable at this time.

In late-1943, the US, UK and British Empire forces invaded Sicily and then Italy. This was again a major bone of contention for Stalin. Churchill was said to have explained this to Stalin by drawing an alligator, showing that the mouth baring teeth was directed at the Soviet Union. It had its armoured back and tail stretched along the north and northwest coast of Europe, but that Italy was where its "soft underbelly" was exposed. Fighting through Italy, Churchill argued, would knock out Germany's junior partner and expose Germany to attack from three sides. However, Italy was actually well defensible in some areas due to the difficult terrain and German forces were able to hold back Allied forces for most of the war once they progressed north in Italy.

It was not until 1944 that the Allies had the equipment, preparation (trained soldiers in sufficient number in the UK from varied Allied forces, sufficient numbers ships from late-1943 when US production was fully running and the u-boat threat in the North Atlantic was increasingly managed, landing equipment, safe supply from the Atlantic, intelligence sources, etc) and plans for invading northwest Europe. The Western Allies were deeply concerned about the potential for failure due to the disastrous Dieppe raid of August 1942, when Canadian units were used to assault a port in France and suffered terrible losses in life and equipment. Therefore very demanding plans were put in place to try to maximise the chances of gaining a foothold in France.

After Western Allied forces landed and began invading Nazi-occupied France, there was the question of which Allied country would get to Germany first. The western Allies were concerned to not let all the fighting take place on the Eastern Front because they wanted to prevent a Soviet occupation of the whole of Germany. They agreed a deal with Stalin to somewhat synchronise their invasions, but Stalin broke the deal in an attempt to get to Berlin first.

Sources:
Phillips O'Brien, "East versus West in the defeat of Nazi Germany", Journal of Strategic Studies
Volume 23, 2000 - Issue 2

Millet & Williamson, A War to Be Won: Fighting the Second World War, 1937-1945 (2000)

Weinberg, A World at Arms: A Global History of World War II (1994)