Wenigstens is a word of positivity, and often optimism and hope. You say it if you're glad that something is at least that level and not worse.
So if you said ..., er sieht wenigstens schlecht aus, this would mean you are glad he looks at least bad. I think this is not what you have in mind and that's why wenigstens is not appropriate here.
In your second sentence it's a good choice to use wenigstens because you appreciate his sorry. That's a positive signal after the bad situation, so hope and optimistic thinking relieved it a bit.
jedenfallsim 2. Satz falsch. Was soll es ausdrücken?Zumindestginge. – user unknown Oct 11 '13 at 01:28