I stand corrected. The transcript of the tape as provided by NICAP does mention weather balloons. The pertinent section is here:

Any balloons?
Yeah.
Not that I know of.
I see. Well, do, uh, does Edwards have a [CLEARS THROAT]
Edwards don't, don't have a rawinsond [radar reflector balloon target] unit? [UNINTELLIGIBLE]
[SOUNDS LIKE: to send up.] So I doubt if they launched anything. They wouldn't have no reason to.
They wouldn't have any reason to send [OVERLAPPING] balloons up ?
[OVERLAPPING] Not the weather section anyway.
Out of Edwards, huh?
No.

This is not talking to the weather section of the base. It is talk between the tower and the Air defense controller. They talk about any RAWIN balloons (which employ radar reflectors). However, contrary to what they state here, it is standard procedure to launch weather balloons at regular intervals during the day (how do you think they got the temperature data in the report for that evening?). Since they did not use radar targets, the balloon would have to be tracked visually, which means it would be lit. BTW,the winds that morning were from between NW and NE (again data measured through the use of a balloon) depending on the altitude. This means the balloon would have traveled towards the South, which is the direction of travel of the one target the UFO officer states was a weather balloon! It did not travel against the wind as you stated earlier.