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Timing is already advanced for optimal power under low load situations, so that's not a factor. The only way a tune will give you better fuel economy under low load is if you lean out the air fuel ratio. Removing your cat will help a little bit too, and a lot of people do that in combination with a tune. More info on fueling, these cars are probably pretty conservative with regard to "protective fueling" which means richer AFR depending on how hot the DME thinks things are. You wouldn't necessarily have to be under high load to incur that, but I'm not very knowledgeable about the N54 / N55 DMEs so I couldn't say how they're mapped. You can observe for yourself the air fuel readings with a logging program. The upstream o2 sensor is wideband stock.
In my last car I experimented with running slightly north of stoich under low RPM / load. Yes, it will give you better fuel economy, but you NEED an EGT gage to do it safely otherwise you're playing with fire.
One interesting thing about direct injection is you can use a method called stratified combustion which gives a locally stoich combustion that's overall lean with respect to the total air in the cylinder. This gives really good fuel economy under low load but the emissions are "unacceptable" so manufacturers don't do it. The DME is capable of making it happen, but it's not a simple remap to enable this and 99% of people getting a tune care mostly about power, so I don't know any aftermarket tuners who offer that feature.
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