Quite a lot of people, you'll find. [img]smilies/smile.gif[/img] Welcome to the forum, hope you enjoy it here... certainly you will find a source of ready Tolkien lore to fulfil your most fervent desires, if that is what you seek.
The answer to your question is found in the Appendices, but I'll explain it in brief here. After the death of Ondoher of Gondor and his sons, Arvedui -- the last king of the Numenorean North-Kingdom Arnor (the ruined kingdom; have a look at your LotR map), made a claim on the throne of Gondor; thus the two kingdoms of Arnor and Gondor would be united, and under the man who could claim the most clear link to the throne (Arvedui, being a king of the North-Kingdom, was descended from Isildur Elendil's son; the kings of Gondor traced their line from Anarion his second son).
The claim was rejected, and the throne givin to the victorious royally-linked Gondorian general, Earnil, instead. The next year Arnor was overrun by Angmar and vanquished. Arvedui perished afterwards trying to escape by sea, in a massive storm. A huge Gondorian force, under Earnur Earnil's son, then joined up with the Elves of Lindon (the Second Last Alliance [img]smilies/smile.gif[/img]?) to destroy the armies of Angmar, but they could not rebuild Arnor and the North was left desolate.
However Arvedui's son had survived, and thus the line of Elendil was preserved in the North unbroken -- by the Chieftans of the Rangers, the wandering Dunedain of the North who survived the ruin of Arnor. They were allied with Rivendell and secretly guarded Eriador.
When Earnur was killed in Gondor without an heir, the rule of the Stewards began. The existence of the northern Chieftans was unknown for long, and if it eventually was was ignored in the face of greater problems. Thus Arathorn was a Northern Chieftan and not a king.
Aragorn II, his son, was the one that rose up and took the crown of Gondor. Mordor defeated, the kingdoms of Arnor (rebuilt soon after), to whom Aragorn was the rightful heir through Arvedui, and Gondor of Elendil, were united under his High-Kingship.
The proposal of Arvedui thus happened eventually, but not for a long while.
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