Belarus wasn't really part of Russian Empire; for centuries it was part of Grand Duchy of Lithuania. No need to evaluate history, because Belarus is its own country regardless of its problems. It is great if a lot of its citizens feel close to Russia or any other country, but there is no need to try to take away their own place from them.
check the map of Kievan Rus, baby
1015-1113 AD ,
since 13th century it's become a part of Grand Duchy of Lithuania, but initially a territory of Kievan Rus
As for Russian-Belorussian relations - http://en.wikipedia.org/wiki/Union_State
as for passports
every Belorussian can get second passport (Russian) if
*has relatives in Russia (wife/sister/grandma etc)
*was born on USSR on territory of Russia
These Belorussians get Russian passports automatic and live in Russia with Russian passport and in Belorussia with Belorussian.
All the rest Belorussian can get Russian citizenship if refuses Belorussian citizenship. But Belorussia doesn't except refusals and they live with 2 passports either.
My Relatives live with 2 passports, but actually with just Belorussian passport you have same rights as with Russian , can live, work for instance in Moscow without any extra permission, just register in 30 days