American weapons to the Ukrainian government would be a world political disaster. It would no doubt cause extreme reactions from the Russians and divide the World along cold war lines.
1) A country has a sphere of interest. This sphere can be microscopic for small countries or big for great powers. Thus the size of this sphere is primarily decided by power. If competing countries have greater power, they can reduce the sphere of interest of a country.
But even if power was all, it can still be unwise to use a transient weakness of a country to overly reduce its sphere. Germany made this mistake vs France in 1871. France made the same error vs Germany on a larger scale in 1918. Of course the reduction can succeed, but used against big peoples it often causes a later surge of power from the defeated and humiliated.
This is a real risk in the case of Russia. Since Gorbatjov she has already been reduced, not only with respect to sphere of interest, but also in the proper territory. Direct American aid in further reducing its sphere in Eastern Ukraine would have a most extreme provocative effect. As old Kissinger is quoted as having said, the fighting is not far from Moscow.
2) The above considerations are based on what could be called a "power-based sphere of interest". Even though it would indeed be naive to overstate its real importance, we can since 1945 also speak of legitimate interests of a country, a "legitimate sphere of interest". Taken the history of the recent decades in Eastern Europe into consideration, it would not be absurd to say that Russia has a legitimate interest in Eastern pro-Russian Ukraine.
3) As said in other posts it is possible to see the West and Russia as belonging to two different civilizations. On the basis of this too it would probably be very wise to respect what is on the eastern side of the cultural border as part of the Russian sphere. Otherwise the cultural difference will contribute massively to the feelings of humiliation and rage in the Russian government and Indeed also in the Russian population.