Claims that the regime has been weakened are false. Cuba is still a one-party state which still persecutes political enemies and seriously restricts freedoms. If anything, the communist regime has become more popular than it would have been due to American sanctions. Due to the embargo, all the problems Cuba has are blamed on US. If the embargo was lifted the government would be held accountable.
Economic sanctions have not harmed the government, they have mostly harmed ordinary people. Cuba has suffered from a lack of food and medical equipment. If the embargo were lifted essential supplies would find their way back to the people even if the government skims some of the profits made in any trade deals. 
The embargo does more harm to ordinary people than it does to the regime. It has not destabilized the government enough to end one-party rule or reduce persecution. The government would be more unpopular if the embargo were lifted.