Generally speaking most inkjets will print 250/300 gsm. The problem usually lies with the feed path, some printers sending the stock through 180 degrees (not good) rather than straight through. Unfortunately the latter usually means a bigger appliance footprint.
The other thing to consider is the 'stiffness' of the stock used. Some 250gsm is more pliable than others, hence easier to feed.
Having said all that I use a HP Photosmart A4 All-in-one (C410b) with 180 degree feeds and it prints up to 300gsm (duplex as well) with no problem.