I actually think the opposite is needed. A weaker president would have less reason to be impeached because Congress could easily overrule him, but a stronger president, whose main check on power is the threat of impeachment and removal, would be more likely to be faced with Congressional opposition.
Also, the removal level needs to be a bare majority as well for this situation to work.
That is a very good point.
Perhaps not a simple majority, but 3/5s of each house or something like that.