Yes, unless you know for sure it's the same barista every time. Even then, it's pointless to even bother tipping at all if it's a dollar once a week.
That said, you can make drip coffee at home, not worry about tip, and spend even less money if that's your concern (hey, I'm poor, that's what I do). Assuming you're spending, what, around a $1.50 for your drip coffee, and you are thereby spending less dollars than pretty espresso drinks, does it kill you to throw in a couple quarters each time for tip? A dollar per week is an insult if you are a frequent customer.