All this talk of "German Hegemony" seems very much based on hindsight. Britain's rivals in geo-political terms were France in Africa and Russia in Asia. Britain's fear of Russian interference in Afghanistan, Persia and Tibet cannot be overstated. As much as they are flights of fancy, these percieved Russian avenues to move on India persisted as a real factor in British decision making for almost 100 years.
And Germany as the most powerful nation on the Continent makes it something is something with any memory of history can recite British policy towards as yourworstnightmare basically addressed.
An army/continentally oriented/threatened Germany is still incredibly mighty:
Germany
alone vs. France/Russia (OTL statistics for 1913):
14.8% of world manufacturing vs. 14.3%
Energy consumption from modern fuels, metric million tons of coal equivalent 187 vs. 116.8
17.6 million tons of steel production vs. 9.4 million tons.
Total industrial potential (UK in 1900 =100) 137.7 vs. 133.9
Austria-Hungary as partner #3 - which has no great reason to want to be allies with Russia more than Germany, and hardly more enthusiasm for France:
4.4% of world manufacturing (so now ahead of Germany)
+49.4 equivalent million metric tons of coal (still behind)
+2.6 million tons of steel (still well behind)
+40.7 total industrial potential (so now ahead)
The only significant advantage this unholy alliance has is manpower to mobilize (using OTL WWI figures, Germany mobilized 13.25 million men, France+Russia is 21.2 million, Austria-Hungary adds nine million)
Why does Britain want to favor the strongest power again?
Diplomacy could and did deal with the Bear and the Frog. Dealing with the Crow (if you don't get the reference, I'll post the link - it refers to the first Reich, but the same principle applies) is another problem entirely.
Not sure its worth adding Italy's statistics given how pitiful they are, but I'll post them if desired.