There are two clues to the symbolic meaning of this ceremony. One comes from the ordination Mass wherein the chasuble is said to signify charity. The second comes from the vesting prayer the priest recites when he puts on the chasuble before Mass wherein the chasuble is referred to as the "yoke of Christ".
In the ordination Mass, when the bishop bestows the chasuble upon the priest he says: "Receive the priestly vestment, which is signified by charity." The chasuble, therefore, is a symbol of charity.
At the moment of the elevations, all are called to adore the God-Man, really present, Body, Blood, Soul and Divinity, in the Blessed Sacrament of the Altar. As those assisting at Mass adore the Blessed Sacrament, a minister at the altar lifts the rim of the chasuble, symbolically signifying that from which all charity flows, namely the God Who dwells among us, Jesus Christ in the Eucharist.
The next is with Altar boys performing the ceremony at low Mass. When putting on the chasuble before Mass the priest recites this vesting prayer: "O Lord, Who hast said, 'My yoke is sweet and My burden light,' grant that I may so carry it as to merit Thy grace. Amen." Thus, as well as being symbolic of charity, the chasuble is specifically referred to as the "yoke and burden of Christ" in the Church's rites. When the deacon lifts the rim of the chasuble at the elevations he symbolically signifies that the God-Man's "yoke is easy and His burden light" (Matt 11:30) specifically because He dwells among His people in the Eucharist.
These more important symbolic reasons for the ceremony can bear much meditative fruit for those assisting at Mass. For this reason, even though the rubrics do not call for the altar boy to perform the ceremony at low Masses, it is a good and upright custom for the faithful. Because of the rarity of solemn Masses today, if it were not for the custom of the altar boy imitating the ceremony at low Masses the faithful would needlessly be denied the ceremony and the symbolic significance attached to it.
Thirdly concerning incense; our present Chapel is so small that the offering of the sacrifice with the additional use of incense in the Low Mass would quickly overwhelm the communicants and precipitate a mass exodus from the area. However, this being said, we attempt to observe as closely as possible the rubrics of the mass with good judgment.