Locomotor can move somewhat heavy objects.
Tonks moves Harry's trunk, with all his school supplies in it, using Locomotor.
“Ah well … wand still in your jeans? Both buttocks still on? OK, let’s go. Locomotor trunk.’
Harry’s trunk rose a few inches into the air. Holding her wand like a conductor’s baton, Tonks made the trunk hover across the room and out of the door ahead of them, Hedwig’s cage in her left hand. Harry followed her down the stairs carrying his broomstick.”
- Harry Potter and the Order of the Phoenix, Chapter 3 (The Advance Guard)
Flitwick also uses it to move Trelawney's luggage back to her room.
“Professor Flitwick went scurrying after them, his wand held out before him; he squeaked ‘Locomotor trunks!’ and Professor Trelawney’s luggage rose into the air and proceeded up the staircase after her, Professor Flitwick bringing up the rear.”
- Harry Potter and the Order of the Phoenix, Chapter 26 (Seen and Unforseen)
Wingardium Leviosa can also move somewhat heavy objects.
Harry used it to lift a motorcycle sidecar with himself in it.
“There was a deafening bang and the sidecar broke away from the bike completely: Harry sped forwards, propelled by the impetus of the bike’s flight, then the sidecar began to lose height –
In desperation Harry pointed his wand at the sidecar and shouted, ‘Wingardium Leviosa!”
- Harry Potter and the Deathly Hallows, Chapter 21 (The Tale of the Three Brothers)
Ron also used it to lift a troll’s club that was heavy enough to knock the troll out.
“Hermione had sunk to the floor in fright; Ron pulled out his own wand – not knowing what he was going to do he heard himself cry the first spell that came into his head: ‘Wingardium Leviosa!’
The club flew suddenly out of the troll’s hand, rose high, high up into the air, turned slowly over – and dropped, with a sickening crack, on to its owner’s head. The troll swayed on the spot and then fell flat on its face, with a thud that made the whole room tremble.”
- Harry Potter and the Philosopher's Stone, Chapter 10 (Hallowe’en)
The Hover Charm can as well.
Hermione used it to lift a heavy chest of drawers.
“Ron was buried deepest: Harry and Hermione climbed, as quietly as they could, over all the wreckage to where he lay, trying to prise a heavy chest of drawers off his legs. While Xenophilius’s banging and scraping drew nearer and nearer, Hermione managed to free Ron with the use of a Hover Charm.”
- Harry Potter and the Deathly Hallows, Chapter 21 (The Tale of the Three Brothers)
Xenophilius Lovegood also tried using it to move a printing press.
“The printing press blocking the stairs was vibrating: Xenophilius was trying to shift it using a Hover Charm. Harry did not know what Hermione was waiting for.”
- Harry Potter and the Deathly Hallows, Chapter 21 (The Tale of the Three Brothers)
A tree is moved using a spell called Mobiliarbus.
On one occasion, Hermione moves a Christmas tree using Mobiliarbus. It worked - so this was effective at moving a tree. In addition, the incantation (from Latin words meaning move and tree) and its subsequent effect imply that it's specifically meant for moving trees. It's only ever used once, so it's not clear if it would work on a tree as big as the Whomping Willow, but it's a possible candidate for tree moving.
“Somewhere above him, Hermione whispered, ‘Mobiliarbus!’
The Christmas tree beside their table rose a few inches off the ground, drifted sideways and landed with a soft thump right in front of their table, hiding them from view.”
- Harry Potter and the Prisoner of Azkaban, Chapter 10 (The Marauder’s Map)
Large structures may be built similar to how they're repaired in Fantastic Beasts.
In the Fantastic Beasts and Where to Find Them movie, Aurors repair the broken buildings of New York with magic.
“Aurors move through the streets, performing Repairing Charms to rebuild the city: buildings and cars are reconstructed and streets are returned to normal.”
Fantastic Beasts and Where to Find Them: The Original Screenplay
It's possible that wizards could do something similar to build new buildings, although they wouldn't already know what the final building is supposed to look like as exactly as when fixing already-existing buildings.