Well a number of reasons really.

Firstly there's the fact that Russia was by far the most influential of those states with both the Ukraine prior to euromaidan and Kazakhstan reasonably within the Russian sphere of influence such that they were unlikely to contest the Russians being considered the inheritor of things like the Soviet Permanent Seat of the Security Council. Under the context of the end of the cold war where the west and the Russian Federation were attempting to establish a new friendlier relationship it was also sensible for the west t recognise this largest and most powerful of the successor states of the Soviet Union as the inheritor of various treaties and things like the Security Council Seat. On the subject of weapons that was primarily a matter agreed upon internally. Much of the weapons that had been in the successor states of the Soviet Union in the other republics remained there of course, for many years many of the former soviet republics used old Soviet arms and other military equipment.

The only notable exception being nuclear arms. The launch codes of most of these weapons remained in Moscow meaning it would have been difficult for those in the Ukraine to have been able to use them in the first place and in general western powers were also caging about nuclear proliferation greater than necessary. The idea basically being the more countries that have nuclear weapons the greater the chance that someone ends up using them. As a result the US mostly supported nuclear arms returning to Russian hands such that they would only have to deal with a single nuclear state. and if there was to be a single country that would hold onto them the logical one would be Russia, it had the most resources, the most influence to acquire them and it was very unlikely anyone was going to be willing and able to force the Russians to give them up to anyone else. Plus they already had the largest number of them anyway. Kazakhstan being pretty solidly in the Russian sphere of influence was happy to exchange the nuclear arms on its soil back to Russia. The Ukraine was more reluctant but being tied closely to Russia and with the United States supporting Russia on this particular matter there was enough pressure to force them to give them up.

Then you have to consider that the centre of power of the Soviet Union was always in Moscow which transitioned into becoming the centre of power for the Russian Federation. Then you have to consider that while the population of places like the Ukraine was not small around 1/2 of the population and 3/4 of the landmass of the Soviet Union became a part of the Russian Federation where the Ukraine had less than 1/5 of the total population. In this it was really the logical choice