If it's a dire, get on the ground asap, then surely the tyres are secondary, presuming a safe landing can be made in the space available? Lets face it, you might be wanting to evacuate once you land anyway.
If it's a situation under control, you can set things up to accommodate the conditions? Including weight.
On the B738, for what it's worth, we can't jettison. So if we depart at max takeoff mass, an overweight landing is the option otherwise, there's almost 13 tonnes to burn down on the B738, or 11.5 once you have executed the take off, emergency turn and handled the problem. Which means Hours of burning fuel. So it's a landing overweight decision, with available field performance in mind.