I think aspects are more important. A house placement will often depend upon the house system you use, especially if there is a late degree rising.
You have to be very cautious about asteroids. The rule is to analyse the majors (the planets) before moving on to the minors (asteroids.)I do use asteroids, but they pretty much have to conjunct a planet before I find them meaningful. There are over 20,000 asteroids out there, and when used indiscriminantly, they can become so much space junk.
For example, I wouldn't deal with the "love" asteroids before fully understanding how Venus and the moon operate in a chart.
Which is holds more weight?
Do asteroids in the houses mean anything?
They're both important but houses are more variable and subjective. Not everyone is going to be majorly affected, for example, by someone's planets falling in their 8th house. Aspects are also variable but more reliable and straightforward.
P.S. The synastry you attached is a little hard to read. Most people here use the inner and outer wheel synastry form.
So, with this synastry, there are no Moon or Venus aspects (only his Venus conjunct my Uranus). So what is making me feel this way towards him? I thought maybe I could get info from asteroids, but since there are no moon or venus aspects, this is just infatuation or just "familiarity" because of our trines? Or maybe just the Uranus/Saturn/Neptune/Jupiter conjunctions I see? It's more of a friendly thing although I feel deeper connections to him and we definitely display sexual attraction towards one another. I am on the outside, he is on the inside.
OK, If I'm reading the aspectarian correctly, and you're on the outside, your suns are trined. Your moon trines his sun. His Venus conjuncts your Mars. Your Jupiter conjuncts his sun. His Jupiter trines your Venus. Since you've deleted the birth times and dates I don't know how accurate your chart angles are, but there are some other inter-aspects going on with them.
I would say your synastry looks pretty good.