Bicycle Mechanics - reverse brake lever help

I switched out my drop bars for bullhorns with reverse/aero brakes. unlike my old brakes, these don't have any sort of spring in them, so when i brake I need to manually push the brakes back up, and the cables are really loose. If i tighten the cables, they rub on the wheels. I have the brake tension turned all the way up. Do reverse brake levers usually have a spring, or are they all like that? Thanks for the help!

The spring is in the calipers, cantis, etc. not the levers. You say you have the brake tension turned all the way up. What does that mean? Pics would help.

Sounds like you have too much friction within the cable housing or in the area where the cable exits the housing at the lever.

I mean the little bolts on the calipers that you can tighten to adjust the tension on each side of the brake. I have those bolts screwed almost all of the way in. When I release the brake, it goes about 3/4 of the way back up, but not enough to keep the pads from rubbing...

+1 There is definitely something wrong here, and it's not the lever lacking a return spring. Your cable slack should be taken up with the pinch bolt on the caliper, and shouldn't bring the pads closer to the rim.

sounds like a kinked cable or cable housing.

regular calipers should have enough spring tension to return the cable and lever to it's original position.

if these are V-brakes or cantis, use the next hole to make the spring open further.
aero levers have a very weak spring in them, not as good as the one in the brakes.

I switched out my drop bars for bullhorns with reverse/aero brakes. unlike my old brakes, these don't have any sort of spring in them, so when i brake I need to manually push the brakes back up, and the cables are really loose. If i tighten the cables, they rub on the wheels. I have the brake tension turned all the way up. Do reverse brake levers usually have a spring, or are they all like that? Thanks for the help!
Return springs in brake levers are a relatively recent thing (last 20 years, say) and mostly came about because the convoluted cable routing under bar tape, through frame tubes, &etc introduced more friction into the system which the lever spring was intended to overcome.

So, check your cable routing to avoid abrupt bends, make sure the cables and housings are in good condition, and in general do things to reduce friction in the system.

My old brakes- springs and loose cables. new brakes- no springs and the cables are under the bar tape. Any suggestions for reducing friction? Thanks guys!

Disconnect cable from brake caliper and feel to see if there's excessive resistance by squeezing the lever while pulling the caliper end of cable by hand.

I'll do that today, if there's a lot of friction but there arn't any kinks, besides redoing the brakes and hoping for less friction, is there anything else I can do? Buy coated coated cables or something?

Check for burrs at the ends of the housing, frayed cable, dinged ferrules, improperly seated housing. I've gotten good results by cleaning and lightly lubing the cables.

I'll do that today, if there's a lot of friction but there arn't any kinks, besides redoing the brakes and hoping for less friction, is there anything else I can do? Buy coated coated cables or something?

My experience is that the extra friction after reassembling is usually caused by having the housing improperly seated in the cable-housing-stop in the lever. You can test for excessive cable friction (as noted above) by detachign your cable from the brakes and pull the cable with one hand and pullthe lever with the other... there should be almost no resistance.

To fix:
-Unwrap the bars, remove the cable and housing (look for any kinks or cripmed ends and fix),
-Re-insert the cable, then the housing -making sure to fully insert and seat the housing into the brake lever... and I believe - although I am not sure - that you should not use a cable-housing ferrule on the lever end of the housing
-anchor the cable housing in place with electrical tape at a few places along the bar where the housing will be under the bar tape.
-test for cable friction by pulling the brake lever with one hand and pulling the cable back through with the other - there should be extremely little force necessary to pull the cabel back and open up the lever
-attach your brakes and test again
-re-wrap the bars

replaced the cables and shortened up the housing a bit, did the trick! Thanks a million guys!!