In this paper we consider the problem of sequence alignment with quality scores. DNA sequences produced by a base-calling program (as part of sequencing) have quality scores which represent the confidence level for individual bases. However, previous sequence alignment algorithms do not consider such quality scores. To solve sequence alignment with quality scores, we first consider a more general problem where the input is weighted sequences which are sequences with probabilities that characters occur in each position. We propose a meaningful measure of an alignment of two weighted sequences and show that an optimal alignment in this measure can be found by dynamic programming. Sequence alignment with quality scores can be solved as a special case of the weighted sequence alignment problem.