Undecidable: $w$ on which a TM M $M$ halts after $\leq w$ steps
Let $M$ be a Turing machine and consider the Turing machine $M'$ that simulates $M$ on an empty input (regardless of the input to $M'$).

If $M$ halts on empty input then $M'$ eventually halts too. This means that there is a word $w$ of sufficiently large length $|w|$ such that $M'$ halts after at most $|w|$ steps (actually, there are infinitely many such words).

If $M$ does not halt, then also $M'$ doesn't halt (regardless of the its input). 

Therefore your problem cannot be decidable as otherwise there would be a Turing machine capable of solving the halting problem.