My brief online search tells me weeping willows can grow to 50ft talk and 50ft wide. Is there a smaller variety that would only be 20-30 feet wide? Or a similarly inviting shade tree that is smaller than a weeping willow?
2With willows of any sort the best question is how close to the house will it be? Tell us more about your requirements and what part of the world you live in– kevinskio ♦Aug 23, 2016 at 17:37
1Also, what qualities of the willow do you find the most inviting? Is it the drooping branches you like? The dappled shade? The general shape of the tree? This will help us suggest alternatives that you might enjoy.– michelleAug 23, 2016 at 21:00
Possibly the weeping flowering cherries - I've seen dwarfs of those, not sure about "mid-sized...? Looks like there may be such "size at maturity" available.– EcnerwalAug 23, 2016 at 21:38
Hi! I'm in Seattle, USA. There is about a 20x20 area of yard, meeting the house only at its corner, that could fit a shade tree. I like the dappled shade, and that due to the drooping branches, sitting underneath it feels somewhat peaceful and private. I'll check out weeping flowering cherries. Thanks!– mevaAug 23, 2016 at 23:59
This link is to a list of small trees for the Seattle area. What you won't see on there are willows. Willows have an aggressive root system and tend to be always dropping leaves and branches.
If you want a tree to sit under you want one that does not shed branches or fruit on you. Wasps and other wildlife are attracted to ripe fruit so I would skip the crab apples.
They list a magnolia but I find that they look great for three weeks and then are dull for the rest.
They also recommend a serviceberry which is a great tree but slow to grow and not very long lived.
The best choices from the list are the smaller maples like Acer ginnala, Eastern Redbud (Cercis canadensis) and the Pagoda Dogwood (Cornus alternifolia).
The last part of the choice is what is available. Start visiting tree nurseries and look at what they have and what shape it is in. No point in buying a tree that has been dried out over the summer. Pass over the ones with poor structure as this defect will not correct itself and can be a cause of failure in later years.
+1 for visiting local nursery. You can check online all you want but ultimately your choice will be decided by what's available locally. That's what I learned the hard way when I planned a whole garden with information online before even setting foot in a nursery.– GillesAug 24, 2016 at 12:05
If you want a weeping tree, you can look at weeping cherries as others have mentioned in the comments. As kevinsky mentioned, any of the fruit trees will attract bees in the spring and wasps when they're in fruit, but personally I've never minded this fact. If you keep the fruit cleaned up, I don't think it is generally unmanageable, and you can always just choose to sit somewhere else when it is in fruit.
There are also a few varieties of weeping beech that are absolutely gorgeous and would be small enough for the space you described. Be careful, though, because there are some varieties of weeping beech that would get too large!
Another option would be a weeping hazelnut, but they may be smaller than what you are looking for - about 10 feet tall at maturity.