If the cross over tube burner has rusted to the point of collapse is a pretty good indicator that it needs to be replaced. I personally, don't see in correlation between LP tank and the collapse of the crossover tube burner. A weak tank, as you called it, would not have any bearing to it.
Now, if you're match lighting the other burners and the flame height remains low, even when turned to high. That's a problem with the grills regulator, which can easily be solved.
Turn the Tank Valve OFF and disconnect the hose from the tank. Wait 5 minutes and reconnect the hose to the tank. Open the tank valve VERY, VERY Slowly (Slow motion, slow), until the valve is fully open. Light the burner farthest from the tank first and turn the burner to HIGH. If the flame height now, looks correct, light the remaining burners the same way. If all the flame heights have returned to normal, you solved that problem.
if it didn't solve the problem, you need to replace the grill's hose/regulator assembly and the crossover tube. The hose/regulator assembly can be purchased at any home center or hardware store, that sells gas grills and accessories. Tank the old one with you for comparison purposes. The Crossover Burner can be purchased from Weber or Factory Appliance Parts
http://www.appliancefactoryparts.com/Hope this aids you in troubleshooting and solving the problem. Please let me know. Thanks and Happy Grilling!!