2 stroke SHOULD be lighter than 4 stroke - the engines are considerably less complex and they create more power per cc. However, economy may be worse.
However, of course, a cheap 2 stroke may be heavier than a decent 4 stroke because lighter materials are used in the 4 stroke.
Consider if you want quiet or not - this will add a bit of weight and cost, but may be considerably more pleasant to use.
As above - do consider how much power you need.
Yes, it's nice to be able to boil a kettle with it - but if you've got gas anyway and the only large thing, probably best to do without.
(From bike racing previously I typically had at least 2.4kw ones, to be able to do two sets of tyre warmers, so there was always plenty of power left over when used in the evening.)