1 general:: Constrain, confine, or limit, as in As long as the children were small, she was too tied down to look for a job. [Late 1600s]
American Heritage Idioms
2 general:: Phrase(s): tie someone or something down to fasten someone or something down by tying or binding. • The robbers tied Gary down so he couldn’t get up and get away. • They tied down Gary., Phrase(s): tie someone down (to someone or something) Fig. to encumber something with someone or something; to make someone responsible to or for someone or something. • Please don’t tie me down to your uncle. Let your sister help out. • Yes, don’t tie me down all week.
McGrawhill's American Idioms And Phrasal Verbs