The most accurate translation may depend on the context, so it would be safer to supply examples. That said, the closest phrase in English may use a variation on "to come with strings attached". "Le mariage est un fil à la patte." "Marriage comes with strings attached." The speaker expresses the view that marriage somehow restricts one's freedom, that it comes along with conditions one needs to fulfill. It isn't as strong as "to be tied up". "Ce contrat est sans risque. Pas de fil à la patte !" "This contract is risk free. No strings attached !" The retailer wants you to believe that said contract doesn't bind you.

it ties us. (you are no more free as a bird, you know have some ties). Google translate suggests "ball and chain" but that seems a bit harsh.

To be tied down = avoir un fil à la patte