There are a variety of reasons why a single word might have more than one possible kanji associated with it. Sometimes the variations represent nuances in meanings, sometimes the kanji in question underwent a reform so one of the alternates is really just an old version, sometimes there's no particular reason except that both version have been used at one point or another.
It's a good idea to research these things with other resources before you decide which kanji to use. 主 is much more common than 重 for おも, when you're talking about the #1 definition.
The reason for why you're also seeing the entry of 主 when searching for 重 is that the word おも, which is normally written as 主, has an alternative spelling that is 重.
If you just want information about one specific kanji, append "#kanji" to your search or click on the Kanji button inside the search bar drop-down menu. Then you'll see this page: http://jisho.org/search/重%20%23kanji
That way you only get information about the kanji itself, and you're not searching throughout the whole dictionary.
Confused about readings!?!
Hello!
I hope someone can help me, when i look up kanji on here it often lists readings with completely different Kanji.
Example, i look up this one 重 but the readings also list 主 - i know both can be read as "omo" ...so i dont know that to do, what i've done lately is to just ignore the readings that use a different kanji. But why do those other Kanji come up there? Is it just because of the way the website or database is setup, because of the identical readings? Or is there actually some kind of connection?
I hope my question makes sense, the one i listed was just one example, there are many like this.
Thank you!