I've been using lumia 920 for a few weeks now. I've read a lot of reviews and the two main criticisms seem to be the weight/bulk (being too heavy) and the app store not having enough variety.

185 grams is not heavy. If you find this is too heavy for a smart phone I suggest you try exercising a little more. Yes this phone might be 50 grams heavier than an iPhone 5 but its 50 grams for every feature being advertised by every competitor, all in one phone.
Currently no other phone can distinguish itself from this by having more key features. 185 grams is a small cup of coffee, that weight is completely fine considering what you're getting. If you weren't getting wireless charging, NFC, physical image stabilisation, huge 2000mAh battery or any of the other stand out features this would be a problem. Considering what the Lumia 920 entails, the weight is remarkably good.

The apps available so far have suited all my needs. There isn't multiple hundred thousand apps here, however I find (at last count I read) 120,000 to be more than enough. If you think you're not going to find what you're looking for, you're wrong. There aren't so many 'fart apps' on this platform. Unlike the competition, Microsoft is careful to only allow quality apps that behave correctly.

Put you doubts to rest, buy this phone.