You are probably focusing on the one who suffers rather than the aggregates themselves being the burden. In SN22.22 we read:
And what is the burden?
Katamo ca, bhikkhave, bhÄro?
The five grasping aggregates, it should be said.
PaƱcupÄdÄnakkhandhÄ tissa vacanÄ«yaį¹.
What five?
Katame paƱca?
The grasping aggregates of form, feeling, perception, choices, and consciousness.
RÅ«pupÄdÄnakkhandho, vedanupÄdÄnakkhandho, saƱƱupÄdÄnakkhandho, saį¹
khÄrupÄdÄnakkhandho, viƱƱÄį¹upÄdÄnakkhandho;
This is called the burden.
ayaį¹ vuccati, bhikkhave, bhÄro.
And who is the bearer of the burden?
Katamo ca, bhikkhave, bhÄrahÄro?
The individual, it should be said;
Puggalo tissa vacanÄ«yaį¹.
the venerable of such and such name and clan.
YvÄyaį¹ ÄyasmÄ evaį¹nÄmo evaį¹
gotto;
This is called the bearer of the burden.
ayaį¹ vuccati, bhikkhave, bhÄrahÄro.
There is also an aesthetic link between the simile in SN15:3 and other suttas. For example, likening the oceans to a collection of tears is not only due to liquidity, but also the taste/rasa. In AN8.20, the Buddhaās teachings is contrasted with the teachings of the asuras through the analogy of the ocean:
The ocean has just one taste, the taste of salt.In the same way, this teaching and training has one taste, the taste of freedom.
SeyyathÄpi, pahÄrÄda, mahÄsamuddo ekaraso loį¹araso; evamevaį¹ kho, pahÄrÄda, ayaį¹ dhammavinayo ekaraso, vimuttiraso.
When they reach the ocean, all the great riversāthat is, the Ganges, YamunÄ, AciravatÄ«, SarabhÅ«, and MahÄ«ālose their names and clans and are simply reckoned as āthe oceanā.In the same way, when they go forth from the lay life to homelessness, all four classesāaristocrats, brahmins, peasants, and menialsālose their former names and clans and are simply reckoned as āascetics who follow the Sakyanā.
SeyyathÄpi, pahÄrÄda, yÄ kÄci mahÄnadiyo, seyyathidaį¹āgaį¹
gÄ yamunÄ aciravatÄ« sarabhÅ« mahÄ«, tÄ mahÄsamuddaį¹ patvÄ jahanti purimÄni nÄmagottÄni, āmahÄsamuddoā tveva saį¹
khaį¹ gacchanti;evamevaį¹ kho, pahÄrÄda, cattÄrome vaį¹į¹ÄākhattiyÄ, brÄhmaį¹Ä, vessÄ, suddÄ, te tathÄgatappavedite dhammavinaye agÄrasmÄ anagÄriyaį¹ pabbajitvÄ jahanti purimÄni nÄmagottÄni, āsamaį¹Ä sakyaputtiyÄā tveva saį¹
khaį¹ gacchanti.
More generally, the puggala who bears the burden is unlikely to remember past lives, but would still bear witness to the tricks of the asuras.