  A $d$-{\em interval} is a union of at most $d$ disjoint closed intervals on a
fixed line. Tardos [Combinatorica 15 (1995), 123-134] and the second author
[Disc. Comput. Geom. 18 (1997), 195-203] used topological tools to bound the
transversal number $\tau$ of a family $H$ of $d$-intervals in terms of $d$ and
the matching number $\nu$ of $H$. We investigate the weighted and fractional
versions of this problem and prove upper bounds that are tight up to constant
factors. We apply both the topological method and an approach of Alon [Disc.
Comput. Geom. 19 (1998), 333-334]. For the use of the latter, we prove a
weighted version of Tur\'{a}n's theorem. We also provide a proof of the second
author's upper bound that is more direct than the original proof.
