PlantFiles: Weeping Cherry Tree, Weeping Higan Cherry
Prunus subhirtella

Not invasive per se. The weeping cherry is grafted onto another trees roots. The suckers you are seeing and pinching off isn't the cherry tree. They are from the parent root. So yes, please pinch them off as they will make you weeping cherry look awful if allowed to grow.

My weeping cherry is most likely original to the house, so almost 60 years old. While not a tall tree, compared to some, it is a very wide tree and needs real space in order to do its thing. I see smaller specimens planted in city front yards and I worry for the tree in the future! The new branches grow down to the ground which I *do not trim* up to look "mushroom-esque", the romance is in the curtain of foliage and flowers! One side butts up to the house, and I do trim a branch or two there so I can be "under" the tree from the house windows. The willow and the cherry are grafted together, creating large bulbous [insert proper botany term here] at their joint. This is where I get some feeder growth, but nothing like the comment below. No red tinges to it either, and certainly nothing invasive! The leaves, while more readily compost-able, do need to be raked aside into beds.

I love my mature Weeping Cherry tree. It blooms beautifully in small pink flowers in early-mid spring, then starts dropping the flowers from mid-late spring. The flowers are tiny, and disappear on their own in a few weeks, so it is not a messy tree like oak or maple. It has smaller, mint shaped leaves in green, with red tinges, which it drops in fall - these do requiring raking or vacuuming, but the volume is considerably less than an oak and is not a terribly large job. My only negative comment about this tree - is it can be considered invasive. It has sent up suckers or shoots all over my garden. It took me 5 years to identify this "weed" as my cherry tree. It's only a major issue in the spring, but pinching off these shoots so I don't eventually have a forest of cherry trees could be a full time job April through early June. It is a truly lovely tree though, just a bit of work to contain it.