It seems to be a function of how likely there is to be residue that would interfere with accurate measurements. Let us look at Rashbam's commentary to the different statements of the Mishnah in to see how this plays out. The earlier part of the Mishnah says:
הסיטון מקנח מדותיו אחד לשלשים יום ובעל הבית אחד לשנים עשר חדש רבן שמעון בן גמליאל אומר חילוף הדברים
A WHOLESALE DEALER MUST CLEAN HIS MEASURES ONCE IN THIRTY DAYS, AND A PRODUCER ONCE IN TWELVE MONTHS. R. SIMEON B. GAMALIEL SAYS: THE STATEMENT IS TO BE REVERSED. (Soncino translation; capitals in original)
Now why does the required cleaning interval differ for wholesalers and producers? Here is Rashbam's explanation:
בעה"ב. שאינו מוכר תדיר כסיטון די בפעם לשנה שאין נדבק בו כל כך
A producer. Since he doesn't sell constantly like a wholesaler, it is sufficient to [clean the measures] once a year as it doesn't stick so much.
חילוף הדברים. סיטון אחת לשנה דכיון דמוכר תדיר אין מתייבש המשקה בתוכו כל כך אבל בעה"ב מקנח כל שלשים דמתוך שאינו מוכר תדיר מתייבש בו השמן שנשאר בכלי ומתמעטת המדה
The statement is to be reversed. A wholesaler [cleans] once a year because since he is constantly selling the liquid does not dry inside it that much, but a producer cleans every thirty days because since he does not sell constantly the oil that remains in the vessel dries and diminishes the measurement.
So far we see that the first opinion in the Mishnah is not concerned that there will be enough residue to make an impact by a producer, while R. Shimon Ben Gamliel is not concerned about that there will be enough residue to make an impact by a wholesaler. Continuing on to the part of the Mishnah that you explicitly asked about, we find the same theme. The Mishnah says:
חנווני מקנח מדותיו פעמים בשבת וממחה משקלותיו פעם אחת בשבת ומקנח מאזנים על כל משקל ומשקל
A SHOPKEEPER MUST CLEAN HIS MEASURES TWICE A WEEK, WIPE HIS WEIGHTS ONCE A WEEK AND CLEANSE THE SCALES AFTER EVERY WEIGHING. (Soncino translation; capitals in original)
And Rashbam's commentary:
והיינו טעמא לפי שהחנוני אינו חייב להטיף ללוקח שלש טיפין כדאמרי' לעיל הלכך מה שמשתייר בכלי נדבק בכלי ומשתייר הרבה והלכך צריך קינוח תדיר אבל סיטון ובעה"ב צריך להטיף שלש טיפין ואין משתייר בכלי כי אם מעט כן נראה בעיני
And this is the reason: For a shopkeeper is not obligated to pour out three drops for the buyer as was said earlier [in the Mishnah on 87a], so that which remains in the vessel gets stuck to the vessel and a lot remains; therefore it is required to constantly be cleaned. But a wholesaler and a producer are required to pour out three drops, so only a little bit remains in the vessel. This is what appears to me.
על כל משקל ומשקל. כל פעם שהוא שוקל שנדבק בו הרבה יותר ממשקלות והלכך על כל ליטרא וליטרא שהוא שוקל צריך לקנח מאזנים
On each weighing. Every time that he weighs, since a lot more gets stuck to it than [gets stuck to] the weights. Therefore for every litra that he weighs he must clean the scale.
Here again we see that the issue is that the scale is particularly susceptible to having residue stick to it; thus, if you don't clean it each time the measurements will be impacted. The other equipment is not as susceptible to residue getting stuck to it, so you only have to clean it at limited intervals when enough residue might have built up to impact the measurements.
Similarly, R. Yehoshua Falk in his commentary to Shulchan Aruch (C.M. 231:18) writes:
ומפני שהדבר לח מונח בכף מאזנים משו"ה הצריכוהו לכף מאזנים קינוח בכל פעם משא"כ המשקל שמונח בכף השניה אין צריך קינוח אלא מפני דהמודד דבר לח נוגע בידו המלוכלכת
And because the moist item is placed on the end of the scale [itself] they therefore required the end of the scale to be cleaned every time. As opposed to the weight which is placed on the other end [of the scale] it is not required to be cleaned except for the fact that the one who measured the moist item touched it with his dirty hand.
Again, the differentiation between the scale and the weights is based on the greater likelihood of residue building up on the scale to impact the measurement. The underlying reason suggested here is that the moist item never comes in direct contact with the weights because the weights are on the other end of the scale. But it does come into direct contact with the scale itself and therefore there is a greater concern for the scale to be cleaned.