"But I think a lot of people are using poverty as a scapegoat for laziness and lack of education or motivation. "
Yes they are. But that isn't a cover all answer why there are 'obese poor'. There is no catch all reason.
Of course there are those that don't have the facilities to cook due to their accommodation or perhaps their oven/hob is broken and they can't afford to replace so have to rely on takeaway foods, but I doubt this group make up a large percentage of the 'obese poor'. (But they are in a poverty trap - money spent on takeaways means no money to gain cook facilities)
If a household not in this circumstance is buying takeaways (as opposed to convince foods from shops) frequently then the excuse of cost is a difficult one to believe. Takeaways are not the cheap option. I'm not sure how many below the poverty line actually do this. I do think there's a belief amongst the wealthier classes that there are greater numbers doing this than there actually are.
There are then those that cannot afford frequent takeaways, and lack transport or nearby affordable supermarket (or both) so ready meals and convinced food from a shop they can get to (beholden to what that shop supplies).
Amongst this group of those lacking transport (which makes weekly shopping difficult - a fact I think many who have not experienced lack of transport ever cannot empathise with and so don't understand) maybe people who do have an Aldi or Lidl near by but lack the understanding of how to cook, and those who don't want to know how to cook or can't be bothered with the time.
There are those who are time poor too, long days and late in the door, too hungry to wait. Of course there is the choice of a slow cooker - this again needs the motivation, knowledge and time.
One of the biggest problems (and this'll be cultural) is the desire to treat ourselves. 'Treats' by their very nature should be infrequent, but there's been a huge increase in how frequently people think they deserve a treat. Its a bit of a chain reaction too, 'everyone' is eating more exciting food (not boring lentils, not boring stews out of a slowcooker etc) so why shouldn't i?
Culturally treats are what in Britain? Unhealthy and quick usually.
There are plenty more situations that are causing this rise in obesity than I've mentioned in my essay of a post. As there are several reasons why it's boys and not girls: many have been touched on in the thread though.