What is a cheap puncture-proof tire against tackweed? Lately, each time I ride my bike around the Bay Area, I get tackweed onto my wheels where upon one or both of them flatten overnight. Most of those are five minute rides to my local library. So, I have had to replace the tube at least ten times already for a two-month period. Details of the situation:


Road Bike that I got from Costco. 
Tire is 700x40c, Kenda (42-622)


I'm not very verse in bicycles, but my final solution is that I need to find a tire that does not get punctured by tackweed. My problem is that I have not found such tires at a cheap price with the right size. By cheap price, I mean something around $25-30 if able; otherwise, I would alright with something less than $70 as long as the size can be fitted onto the rim.
Forget the slime, thornproof tubes, and tire liners.  IMO, the best puncture protection for under $40 are Vittoria Randonneurs.  I've had excellent luck with them.  I had a pair of Gatorskins before the Randonneurs, and trust me, Kevlar belts do not work as well.  Because the Kevlar is a woven material, very sharp objects can penetrate between the Kevlar fibers.  Happened to me at least six times with the Gatorskins over a two year period.  Blackberry thorns, glass, and even staples penetrated the Kevlar.

Also, since you say you're not very versed in bikes, I have to wonder if you may be pinching the tubes when mounting them, or leaving whatever punctured the tube in the tire, allowing the next tube to be punctured as well.  Are you checking for any sharp objects poking through the inside of the tire, or for any burrs along the inside of the rim?  I always try to find the puncture in the tube before removing it from the rim, so I can concentrate on that area of the tire for a closer inspection.