Gawk not filtering out larger number?

Your awk command performs lexical comparison rather than numerical comparison, because the RHS - the price value - is enclosed in double-quotes.

Removing the double-quotes would help, but it's advisable to reformulate the command as follows:

 gawk -F '\t+' -v price="$price" '$5 <= price' file

The shell variable $price is now passed to Awk using -v, as Awk variable price, which is the safe way to pass values to awk - you can then use a single-quoted awk script without having to splice in shell variables or having to worry about which parts may be expanded by the shell up front.

Afterthought: As Ed Morton points out in a comment, to ensure that a field or variable is treated as a number, append +0 to it; e.g., $5 <= price+0 (conversely, append "" to force treatment as a string).
By default, Awk infers from the values involved and the context whether to interpret a given value as a string or a number - which may not always give the desired result.

You're really calling a separate gawk for each column? One will do:

gawk -F "\t+" -v OFS="\t"   \    -v city="$city"         \    -v bedrooms="$bedrooms" \    -v space="$space"       \    -v price="$price"       \    -v weeks="$weeks"       '        $2 == city && $3 >= bedrooms && $4 >= space && $5 <= price && $6 <= weeks {            $1 = $1; print        }' listing |sort   -t $'\t' $sortby $ordering |column -s $'\t' -t

(This is not an answer, just a comment that needs formatting)

The $1=$1 bit is an awk trick to make it rewrite the current record using the Output Field Separator, a single tab. Saves you a call to tr