The official reasons and goals for the Russian anti-Prussian policy (which eventually led to the Russian entry into what became the 7YW) had been formulated in a protocol of the "Conference at the Imperial Court" (basically, council of the ministers) dated by March 15, 1756. I finally found the text at
http://www.vostlit.info/Texts/Dokum...ilet_vojna/Materialy_russ_arm_flot/1-20/2.htm
The stated goal was not to allow further strengthening of the King of Prussia by cutting down his forces to such a degree that it will not be a danger to the Russian Empire.
Due to the obvious (to the "conference") fact that Russia can't fight Prussia alone, the Court at Vienna had to be convinced to join the effort.
Poland must be prepared to the fact of the future passage of the Russian troops through it territory and, as a reward for a good behavior, it should be told that because her imperial majesty does not look for any territorial gains for herself and just wants to weaken the king of Prussia, Poland will be rewarded with the Kingdom or Prussia (in context: "Eastern Prussia") if the Russian troops manage to conquer it. (Item 4 of the "methods" part of the Protocol).
In the unitemized part of the protocol dedicated to the general possibilities ("one can't either predict or guarantee the success on the scope we desire") were listed potential options like return Silesia to Austria (as one of the mays to weaken Fritz) and territorial swap with the PLC: as a gratitude for delivery of the Eastern Prussia the PLC may give Russia Courlad and the territories "which will eliminate the constant problems we have with them now" and perhaps even "a way to connect the commerce of the Baltic and Black Seas thus taking control over almost all Levantine trade" (taking into an account that at that time the PLC did not have an access to the Black Sea and that Russia at that time did not have any sizable merchant navy anywhere, this gives an idea about the general competence of the "Conference").
While superficially reasonable, the underlying assumption (Prussia representing a danger to the Russian Empire) was all smoke and mirrors because Prussia would not and could not attack Russian Empire. What all that lofty talk really meant is that growing Prussian strength makes it potential Russian competitor for the influence in the PLC (which Russian government already considered as more or less its own backyard).
Not to mention that as soon as conquest of the Eastern Prussia became a reality (somewhat to the Russian surprise: nobody expected that Frederick would leave it practically undefended) its population was immediately forced to swear loyalty to Elizabeth and that Russian operations during the later part of the 7YW had been heavily concentrated on providing a base in Pomerania (just to give it away?) instead of being directly engaged against Frederick (one of the reasons that allowed him to somewhat restore his positions).
An additional (and perhaps more important) consideration was Elizabeth's personal dislike of Frederick who was making (quite correct) remarks about her mental abilities. She was at that point supported by her Chancellor,
Bestuzhev-Ryumin, who (as a man of principle) was taking the bribes only from the Austrians (and, IIRC, the Brits). "Conference" consisted mostly of the carefully selected "yes men" some of whom, like Count Shuvalov (supplier of pretty much everything including Russian artillery), had been interested in a military conflict.
What if, Fritz managed to control his tongue AND the issue of his potential designs regarding the PLC was not considered by Elizabeth and her ministers as important as it was in OTL? After all, security of the PLC could be guaranteed by the explicit defensive alliance.
So Russia is out of the picture while all other European powers are happily fighting each other. What are the possible outcomes in Europe?