No, Barack Obama did not weaken the US internationally. Obama took in some ways a less aggressive, and in some ways a more aggressive interpretation, of the US’s role in the world.
In terms of being less aggressive, Obama didn't engage in any major sort of military operations on the same scale as the Iraq War. But on the other hand, he did expand the scope of US covert operations globally: we need only look at the drone programme and the amount of controversy it generated.
https://www.youtube.com/embed/c9-0p3Z0YUY?wmode=opaque
The Obama Administration presided over an era of mostly consistently high military budgets – which is usually what people refer to when they refer to any sign of weakening in the United States. In his second term, a sequestration kicked in and this began to lower military budgets somewhat. But this was agreed between Obama and Congress which at the time was in the hands of the Republicans. So I don’t think you can entirely lay the sequester on his doorstep. In any case the US military still remains far and away the most powerful in the world.
"I think Trump will take a harder line on China – and from what’s being reported in the Chinese media, Beijing will take a harder line on Trump once he assumes power."
During the Obama Administration, the world was changing in ways the US had no control over. For example, China’s economy was growing. Beijing was spending more money on the military regardless of what the US did. And any reasonable US president who wanted to spend any money at all on domestic programs – which, after all, is what maintains a strong economy – wouldn't have been able to maintain the relative edge the US had over its major competitors in the likes of the 1990s.
What will Trump do about the United States position internationally? Honestly? It's really difficult to know. I think he will take a harder line on China – that’s very clear at this point – and from what’s being reported in the Chinese media, Beijing will take a harder line on Trump once he assumes power.
https://www.youtube.com/embed/RDrfE9I8_hs?wmode=opaque
But it’s not clear whether the long term impact of that harder approach will be. It could go two ways: the US and China could become locked in a trade war and edge closer to a shooting war over territorial disputes. Or the US and China could somehow manage to come to some stable, long-term agreement based on a shared acceptance of each other’s interests.
Donald Trump doesn't have a record of public service, so at the moment it’s really difficult to second-guess how he’ll deal with the inevitable challenges that any presidential administration faces. It’s possible that his transactional approach could well pay dividends in terms of undoing some of the aspects of US foreign policy which are no longer fit for purpose. Or he may end up getting blindsided by people who simply have been doing this for much longer, and have thought about it in much more sophisticated terms, than he has.