The corruption watchdog found that Sri Lanka was the 92 worst corrupt nation in the world, in a report released earlier this month.
Police said a grenade had been thrown to the upper floor of Weliamuna's house but no one was injured. Another grenade had been found on the premises.
The Hong Kong based Asian Human Rights Commission (AHRC) said Weliamuna had appeared in many sensitive cases related to corruption and abuses of human rights, extra judicial killings and victims of torture.
AHRC said last month the Supreme Court had issued orders on a case where he had appeared for a man who had complained of attempted assassination by some police officers.
"This attack is chilling but not surprising," AHRC director Basil Fernando, said in a statement.
"Threats and attacks are targeted at everyone who tries to highlight the abuses of politicians and state officers.
"Now senior lawyers themselves are being targeted for nothing other than being engaged in their professional duties to their clients."
The AHRC said the previous day he had raised the issue of a lawyer who had received death threats on a case of bribery and torture related to police officers at the Bar Association of Sri Lanka, the island's top association of lawyers.