Unless the enemy Barik is using the Fortify Legendary card, his Barricade only has 5000 Health. It can sometimes be more advantageous to simply destroy the Barricade instead of sidestepping it.
Tinkerin' Barik has range slightly beyond the level of Viktor. Don't even bother 1v1ing him if he even has 1 turret up, as he then requires multiple people focus firing him to bring him down.
Nearly every Barik out there has a healing card in their loadout. It provides him a heavy sustain. Cauterize is an all around counter that also works against him very well in that aspect, even without a healer on enemy team!
If Barik is running One Man's Scrap on a high level try to use CC (To prevent Barik destroying them himself) and avoid the turrets to prevent this form of healing.
Barik's primary shot is joke from far away, use this to your advantage and force the Barik to either stay in place and try to wait for help or go after you. Be ready for both of these options.