Something like this?

#! perl -slw
use strict;
use List::Util qw[ sum ];

sub ave{ (sum( @_ )||0) / (@_||1) }

my @intervals = map[ split ], do{ local @ARGV = 'intervals.dat'; <> };
chomp @intervals;

my @markers   = do{ local @ARGV = 'markers.dat';   <> };
chomp @markers;

my %groups;
my $first = 0;

for my $int ( @intervals ) {
    my( $start, $stop, $val ) = @{ $int };
    
    ++$first while $first < $#markers and $markers[ $first ] < $start;

    my $next = $first; 
    
    push @{ $groups{ $markers[ $next ] } }, $val
        while $next++ < $#markers and  $markers[ $next ] < $stop;
}

for my $marker ( @markers ) {
    print "$marker ", ave( @{ $groups{ $marker } } );
}

__END__
C:\test>947611
10150 0
10250 0
10350 0.772
10450 0.594666666666667
10550 0.60125
10650 0.60125
10750 0.5585
10850 0.585333333333333
...
18150 0.37475
18250 0.571
18350 0.523166666666667
18450 0.499
18550 0.4958
18650 0.4958
18750 0.372
18850 0.333714285714286
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