It looks like a weeping cherry. The branches are meant to hang down low. If you cut them back you will ruin the shape of your tree. Google image 'weeping cherry' and see how good a well-grown specimen looks.

sam_md -- wow, great call on the spicebush. i would have never figured that out. i scraped a small part of a stem and there was an unmistakable spicy fragrance. it is also planted in a semi shady area, under part of the canopy of a neighbor's larger bush. the leaves on the second one are silvery to blue-silvery on the underside. i really doubt it to be an invasive because the prior owner, who was here through last august, was a very active gardener. i have found a few unusual plants like the cupplant that he must have planted. i think he shopped a lot from prairie moon nursery, finding unique and native-type things.

Check out the Lars Anderson Bonsai Collection describing Chamaecyparis obtusa 'Chabo-hiba' in octopus style at the Arnold Arboretum. Here is a link that might be useful: Arnold Arboretum hinoki

Not a big tree to begin with and very slow growing. After many years it might be as tall as some larger Japanese maples. It is rare to see even mature ones in this area much more than 20-25'. Also a rather expensive little tree and generally sold in smaller sizes for best price point,