Mishna Bikkurim 3:8
The Gemara in Bava Kamma (92a) explains that when the Mishna says the baskets were given to the Kohanim, that only refers to the willow baskets brought by the poor. The previously mentioned "baskets of the wealthy" were returned to the people who brought them. The Gemara says that this is the sort of thing that makes people say "בתר עניא אזלא עניותא", poverty doggedly follows the poor. Rashi explains that it is an ironic truth that bikkurim ultimately costs the poor people more than it costs the rich people, since the poor don't get their baskets back.
Tosfos Yomtov in Bikkurim brings the Gemara (Moed Kattan 27b) that says
The Tosfos Yomtov answers that the glorious spectacle of the rich bringing their precious baskets reflected honor on the Beis Hamikdash, and this is an avodah, and as such it outweighs the issue of embarrassment.
He then asks, what stopped the poor from taking their baskets back? Just as the rich took their baskets back, so too the poor should do so, and so we wouldn't ironically say "בתר עניא אזלא עניותא" , that the mitzva costs the poor man more than the rich man! He answers that there is a general requirement that gifts to the Kohanim be substantial. Since the poor man's Bikkurim is likely a few fruits, only together with the baskets is it substantial enough to be called a Mattanah. The rich man, on the other hand, brings a whole cornucopia, and the fruit alone is a Mattanah.
Reb Yitzchak Chiyos (Chidushei Maharich in Mishnayos) answers that in the Torah it says ולקח הכוהן הטנא מידך, and a Teneh is specifically a willow basket. You see that the Torah is alluding to this specific type of basket and stating that if such a basket is brought, it becomes part of the Mattanah, but only if it is a Teneh. He suggests, as does the Tosfos Yomtov, that this din stems from the requirement that the Mattanah be a davar chashuv.
The Baalei Mussar have their special approach to the question from the Gemara in Moed Kattan. Reb Aharon Bakst, in his Darkei Mussar, says that if the Kohen would remove the poor man's fruit from the basket, everyone would see a yeshivishe shalach manos- a fig, a few stalks of wheat, maybe a date or two. This meager Bikkurim would be embarrassing; everyone is watching, looking at the extravaganza of beautiful and abundant Bikkurim gifts, and the poor farmer would wilt under the dismissive looks of the assembled crowd. (My father Zatzal used to say that when it says about Shimon and Levi כי באפם הרגו איש, it means that you can kill someone with your nose. People can be mortally wounded by a wrinkled nose or a supercilious glance.) In order to maintain the dignity and pride of the poor farmer, it is best that the Kohen just do the ceremony and leave the fruit in its basket, so the person can say to himself that he did the best he could, and it will be precious in Hashem's eyes.
Reb Yaakov Neiman of Ohr Yisrael answers that the baskets of the rich were unworthy, since they bespoke pride, and they were lacking זבחי אלקים רוח נשברה. This is why the Kohen would return the basket to the person that brought it. The humble basket of the poor man, given with a whole heart and a desire to do his best, is more precious than silver and gold.
I'm not sure where to put this answer- among the Baalei Mussar or the Lomdim- but I think it's the best of all. Reb Meir Bergman writes that the Gemara in Brachos (48b) says
This Gemara was in middle of discussing Birkas Hamazon, and the mefarshim puzzle about this passuk, since the parsha of Birkas Hamazon has no such passuk. The Rashash says that Rebbi Meir is reorganizing the passuk that says ובירכת את ה אלוקיך על הארץ הטובה אשר נתן לך. Rav Bergman says that it is not the passuk from Birkas Hamazon, it is the passuk from our parsha of Bikkurim, 26:11, that says ושמחת בכל הטוב אשר נתן לך יהוה אלוקיך ולביתך. The words Hashem and Elokecha show that one must be happy with all that Hashem gives, whether good or bad, whether a lot or a little. (The main Gemara about כשם שמברך, in Brachos 60, uses a different passuk, but that doesn't matter, because Reb Meir might darshen this passuk, which is, in any case, similar to the other passuk on daf samach which also darshens Hashem and Elokecha.)
Rav Bergman says that the lesson of our passuk, that teaches us to understand and appreciate that whatever Hashem gives or takes away is because of His will and His divine justice and mercy, is particularly apt to the idea of Bikkurim. A farmer is expected to take the precious first fruit of his labor and give it away to a kohen, to whom one apple is no different than another apple. One can only do that when he realizes that he is merely a steward of the land, and that the success or failure of his land is purely Hashem's decision, because Hashem is the true owner of both the land and the farmer and is the sole determinant of his success or failure. If so, if the essential message of Bikkurim is hakaras hatov to the Ribono shel Olam, and blessing Hashem no matter what Hashem gives us, it would be totally inappropriate to make a takana so that the poor should not feel diminished by their paltry and meager fruits: what the rich man brings, what the poor man brings, it is all because Hashem decreed that it should be so, and we cannot know Hashem's reasons, but they are all ultimately for the good. Bikkurim would be the least appropriate place to hide the differences between the rich and the poor.
After seeing all of these answers, the question that remains for me is this: We find this concept of avoiding the embarrassment of others in many places. For example;
Some say that this is the reason we hak ohp a chassan at Sheva Brachos, so the ignorant won't be ashamed.
Under which circumstances do we institute such ordinances? Of course, many kehillos have made their own takanos, such as no more diamonds for Kallos, a limit on wedding expenses, and so forth. Do we say that nobody should come to shul in hand-made suits, so as not to embarrass those of us that shop at Marshall's? I know a young man that told the girl he was dating that he had spent Three Hundred American Dollars on the tie he was wearing. (Although she managed to avoid retching, she never went out with him again.) Is that OK? What about girls in a high school: should they wear uniforms so they don't obsess about disparities in the quality of their clothes? Or Esrog boxes, or cars, or ataros, and so forth until you decide the Communists were right and all inequality must be eliminated, or at least hidden? Obviously, this is something that needs to be decided by wise leaders. I wonder if there's any consistency in application.
So here's a few words from an article in the Zomet's Institute's Journal, Techumin. The author is Baron Immanuel Jakobovits , former chief rabbi of Britain