才 marks the number as low, short of expectation (才十一歲 = only eleven). 就 marks it as high, more than expected (就十一歲了 = eleven already). Same age, opposite verdict: 才 points the slope down, 就 points it up.
只 restricts to this item and no other (只買一個 = bought one and nothing else). 才 judges the amount itself as too small. 只 counts; 才 grades.
你十一歲。(flat, no judgement) → 你才十一歲。(only eleven, surprisingly young)
你才十一歲了。 → 你才十一歲。(no 了 — 才 holds the value low, it does not close the count)
他才有三本書。(a mere three, judged too few) → 他只有三本書。(plain restriction: only three, nothing more)
English 'only' covers both the low-amount sense and the restriction sense, so learners reach for 才 where 只 is meant. 才 carries a verdict that the number is too small; 只 simply fences off everything else.