וְאֶקְחָ֨ה פַת־לֶ֜חֶם וְסַעֲד֤וּ לִבְּכֶם֙ אַחַ֣ר תַּעֲבֹ֔רוּ כִּֽי־עַל־כֵּ֥ן עֲבַרְתֶּ֖ם עַֽל־עַבְדְּכֶ֑ם וַיֹּ֣אמְר֔וּ כֵּ֥ן תַּעֲשֶׂ֖ה כַּאֲשֶׁ֥ר דִּבַּֽרְתָּ׃
И я принесу кусочек хлеба и останусь у тебя на сердце; после этого вы перейдете; потому что вы пришли к рабу своему.' И они сказали: 'Так и делай, как ты сказал.'
Rashi
וסעדו לבכם AND SUSTAIN YOUR HEARTS — In the Torah, the Prophets and the Hagiographa we find that bread is the sustenance of the heart. In the Torah. “[And I will fetch a morsel of bread] and sustain your heart.” In the Prophets: “Stay thy heart with a morsel of bread” (Judges 19:5). In the Hagiographa: “And bread that sustaineth man’s heart” (Psalms 104:15). R. Hama said: Here is not written לבבכם but לבכם thus teaching that the evil inclination has no power over angels (Genesis Rabbah 48:11)
Chizkuni
כי על כן עברתם על עבדכם, “for surely that is the reason that you passed by your servant;” Avraham indicated that it was not the habit of travelers to skip the main meal which is normally consumed at noon. He indicated that he realised that they were modest and bashful, and had not asked for any food or drink.
Ramban
FORASMUCH AS YE PASSED BY. Since your path crossed near me, it is not proper that you should not rest a little with me.
So do, as thou hast said. This is an ethical expression indicating that a morsel of bread will be sufficient.85Since it should have stated, “We will do as thou hast said,” and instead it says, “So thou do, as thou hast said,” Abraham ibn Ezra takes it to mean “So do, as thou hast spoken: And I will take a morsel of bread, and do not trouble thyself for more.” Thus the language of Rabbi Abraham ibn Ezra.
It may be that the verse is stating, “So shalt thou do to us, that we recline under the tree and pass immediately as we are messengers, and therefore do not detain us by making us come into the tent or lodge with you.”
So do, as thou hast said. This is an ethical expression indicating that a morsel of bread will be sufficient.85Since it should have stated, “We will do as thou hast said,” and instead it says, “So thou do, as thou hast said,” Abraham ibn Ezra takes it to mean “So do, as thou hast spoken: And I will take a morsel of bread, and do not trouble thyself for more.” Thus the language of Rabbi Abraham ibn Ezra.
It may be that the verse is stating, “So shalt thou do to us, that we recline under the tree and pass immediately as we are messengers, and therefore do not detain us by making us come into the tent or lodge with you.”