As noted, it is mostly the cheap and light portion of data which is more of a challenge.

If you only need a few MB per country just a few times each year, a pan-international roaming sim might be ok. There's also prepaid sims which roam regionally if you plan on traveling mostly to Europe vs parts of Asia.

For more data with wider options but slow on an annual cost, TMobile Simple Choice data only plan or Google Fi run about $20-30 per month.

A dual sim phone like Moto G dual (smaller screen = weight savings) or Asus Zenphone is a decent option if you want to put a roaming sim in one slot with the option of a local sim in the other. You can search for devices by weight and network frequency support here:
http://www.gsmarena.com/search.php3
Add an inexpensive battery pack or search for high capacity/replaceable battery.

One thing I'd advise when looking for an inexpensive travel smartphone - check the build quality of the sim slots, either via YouTube reviews/unboxings or in person. Some of the really cheap phones (cough cough Lumia 520) have scratchy sim pins. If you are swapping sims in and out, plus want to keep them in nice condition, get something with decent build quality. You don't want a pin to break off or sim to get stuck, as finding the right data solution can be the tricky part.