A "favor" is doing something for another person that the doer has no obligation to do,for example, going to the store for a friend or mailing some letters so that a sick friend wouldn't have to go out in the rain. Since a favor involves doing sonething extra,it requires an expression of thanks. It is appropriate to thank the person again after the favor has been done.For a "bigger" favor,that is, one involving more time or effort ,the beneficiary may also give a gift to the doer of the favor. For small things, such as holding open a door ,a person simply says"Thanks".
Always thank someone who offers to help you, whether you accept their help or refuse it politely . When refusing an offer of help , you may want to say something like:
NO,thank you .
NO,but thank you for offering.
Thank you,but I'll manage OK by myself.