First, Amazon's Fire 7 is not a viable option. The Fire 7 works well as a secondary tablet, something to take on a commute/travel or a child's tablet. For a primary tablet, it is just too slow and its paltry 1 GB RAM makes multi-tasking frustrating. This means, as a primary tablet, the choice is restricted to either the HD 8 or HD 10.
In my view, while the Fire HD 10 is clearly the better overall tablet and the one to choose, the answer also depends on the needs and preference of the end-user. If preference is for a compact and lighter tablet then the HD 8 is the better option. The Fire HD 10 is a large and relatively heavy tablet (the issue isn’t just the screen size – large top and bottom bezels make the device awkward to hold). The HD8’s screen is a downgrade, in comparison to the HD 10, but that doesn’t mean it is a poor one.
If size/cost is a non-issue then the Fire HD 10 is the tablet to choose - it is faster, comes with more RAM and the screen is far better. The Fire HD 10, for its size, is not the heaviest large tablet (the device weighs 500G). In comparison, the Samsung Tab A 10.1 weighs 565G and the 9.7 inch Apple iPad weighs 469G. In other words, if the end-user prefers a larger tablet or doesn’t need something more compact then the Fire HD 10’s weight shouldn’t be a major issue – its weight falls within the category average of larger tablets. Its form-factor makes it awkward to hold but this is a minor issue.