What workup do you recommend for patients requiring higher-than-expected levothyroxine doses for their weight?  

I start off with making sure they are compliant, by calling the pharmacy and looking to see if refills are on time, and also see if they are taking it properly and away from medications or food that will  impair absorption. 

If someone is on a significantly greater than expected dose of levothyroxine for their weight, I take a careful history to confirm they are taking the medication appropriately. Usually, the issue is mistiming of medication with regards to proximity to food or supplements - or even simple nonadherenc...