I squeezed a tire replacement on my truck through the States as part of my week long vacation. Tires came out to my personal exception so no issues. Got them at Dunn's Tire. Tirerack was cheap but by the time they shipped them even to a local place for mounting it turned out to be more expensive.
I've never seen any customs folks bend over and check your tires. At one time if you purchased tires near the border rumours had it where those shops would call up the border and advise the plate and tires purchased as some sort of snitch line.
On another note I didn't know they actually weigh your vehicle going through the border. Is this something new?
'05 GMC Sierra SLT Z71 CCSB 4x4
'02 Regal LS
'00 740i Sport