New Post: Mixed shipping - at a loss

I'm stuck (and a little confused) with a new shipping requirement for a site I manage. Currently all products (flowers) have shipping set by London postal codes with a flat rate for anything outside of London. This configured under 'Shipping / By Country'.

Now there's a requirement for larger items (garden furniture) which should have a flat shipping rate of x.xx.

I've tried several things including setting a weight for my test product and then adding a new weight based shipping method, but these costs don't show when I make an order. Instead I get the default country costs from my standard shipping template.

Specifically I'm not clear about...
i) How are the shipping methods invoked? If there's a 'trigger weight' set on a product, should this make the new shipping method automatically apply?
ii) What happens in the case of a mixed order (i.e. flowers and furniture)?

Thanks in advance,
Will