You need to know your VM name. It can be checked with:
> VBoxManage list vms
"YOUR_VM_NAME" {385e587a-ad47-4d36-a734-a126b9e04590}
Usually vagrant boxes comes with VMDK type storage which cannot be resized.
You need to convert the format to resizeable VDI.
> VBoxManage clonehd \
"/root/VirtualBox VMs/YOUR_VM_NAME
/packer-virtualbox-iso-1459796137-disk1.vmdk" \
"/root/VirtualBox VMs/YOUR_VM_NAME/packer-virtualbox-iso-1459796137-disk1.vdi" \
--format vdi
0%...10%...20%...30%...40%...50%...60%...70%...80%...90%...100%
Clone medium created in format 'vdi'. UUID: 67985552-a3e5-4fad-aedd-82565ac963d4
packer-virtualbox-iso-1459796137-disk1.vmdk is a hdd disk file. Your file name can differ slightly.
packer-virtualbox-iso-1459796137-disk1.vdi is new disk file that will be created in VDI format.
Now it's time to resize the disk image.
> VBoxManage modifymedium \
/root/VirtualBox\ VMs/YOUR_VM_NAME
/packer-virtualbox-iso-1459796137-disk1.vdi \
--resize 163840
0%...10%...20%...30%...40%...50%...60%...70%...80%...90%...100%
163840 is new disk size in MB. Now you need to convert the disk image back to VMDK.
> VBoxManage clonehd \
"/root/VirtualBox VMs/YOUR_VM_NAME
/packer-virtualbox-iso-1459796137-disk1.vdi" \
"/root/VirtualBox VMs/YOUR_VM_NAME/packer-virtualbox-iso-1459796137-disk1.vmdk" \
--format vmdk
0%...10%...20%...30%...40%...50%...60%...70%...80%...90%...100%
Clone medium created in format 'vmdk'. UUID: 9f433356-976c-422b-b7f1-2e1279cec993
Run the VM (for example: `vagrant up`). In our case it is a Windows machine.
That's why you need to go to the guest system and increase disk size there.
Open Disk Management `diskmgmt.msc`. Right click on allocated partition and click Extend Volume.