beleaguer vs besiege

To besiege; to surround with troops. 

To exhaust. 

To vex, harass, or beset. 

To beset or surround with armed forces for the purpose of compelling to surrender, to lay siege to, beleaguer. 

to assail or ply, as with requests or demands. 

To beleaguer, to vex, to lay siege to, to beset.