Even though it is not good to be a burden on others, in close relationships, being able to receive kindness and service is a part of the relationship.  People want to feel needed and want to have the opportunity to give to those whom they love or regard.  Sometimes, resistance to love and intimacy hides behind false piety.  

It can be a kindness to also accept, not just to give. Our Gemara on amud aleph tells us:

אָמַר רַבִּי חִיָּיא בַּר אַבָּא אָמַר רַבִּי יוֹחָנָן כׇּל הַמּוֹנֵעַ תַּלְמִידוֹ מִלְּשַׁמְּשׁוֹ כְּאִילּוּ מוֹנֵעַ מִמֶּנּוּ חֶסֶד שֶׁנֶּאֱמַר לַמָּס מֵרֵעֵהוּ חָסֶד 

Rabbi Ḥiyya bar Abba said that Rabbi Yoḥanan said: Anyone who prevents his student from serving him, it is as if he withheld from him kindness, as it is stated: “To him that is ready to faint [lamas], from his friend kindness is due” (Job 6:14). Rabbi Yoḥanan interprets this to mean that one who prevents [memis] another from performing acts on his behalf, prevents him from performing the mitzvah of kindness. 

The Pele Yoetz (“Toreach”) captures the tension between the importance of accepting acts of service versus not being a burden.  He writes the following in relation to  student serving a master, a child serving a father, and a wife attending to her husband:

A man should behave with his sons and his wife and with any person, if he sees that they love and desire to serve him in order to fulfill a mitzvah that is imposed on them or out of love of kindness, then he can direct them to serve him. But if he sees that they do it out of embarrassment or pressure, then he should not bother or burden them...everything according to the nature and dispositions of the members of his household. 

He goes on to spell out how for some people, having the chance to take care of a rebbe or loved one feels like an opportunity and is no burden at all, and for others it is oppressive.  He says, in general, one must assume that he is a burden to others and seek to minimize how much he puts on others.  Even so, with the right person, it is important to allow them to do things for you, as this is their way of serving Hashem.

The Pele Yoetz didn’t use contemporary psychological terms, but I do believe that, between the lines, he is addressing those who have a fear of accepting service and goodness from loved ones.  A good relationship is built on small, voluntary and caring acts of kindness that you do for each other.  This is an important bonding mechanism that should not be ignored.  In a marriage, one should not say Mishle (15:7) “שׂוֹנֵ֖א מַתָּנֹ֣ת יִחְיֶֽה one who disdains gifts shall live long.”  To the contrary, allowing yourselves to accept each others’ kindness creates greater intimacy and connection.