Has the derandomization of slightly non-uniform classes, e.g BPP/linear, been studied? By BPP/linear I refer to BPP machines with linear advice, which fulfills the promise when given the "correct" advice, 
and the derandomization should give us, say, a P/linear or (SUBEXP/linear) algorithm.

If we use non-uniform assumptions, I think classical results should work, because we can "fool" non-uniform adversaries.

However, using uniform assumptions, say $EXP\neq BPP$,  non-trivial derandomization seems like a harder question.

Do there exist results regarding this kind of classes, not necessary BPP/linear?
I used the this scholar search, and the only result which seems somehow relevant is this:

Lance Fortnow, Adam Klivans, Linear Advice for Randomized Logarithmic Space, ECCC TR05-042, 2005.

Unfortunately, I think it is not exactly what you need. In particular, the main result of the paper is $\mathbf{RL} \subseteq \mathbf{L}/O(n)$. Yet I believe the techniques used there might be helpful in the case of your question.