I’ve been practicing by going up my driveway (apprx. 150’) but at the top I experience severe leg “burn” and can’t continue. When I get to the flat road at the top my legs really hurt. It feels like I just completed 25 reps on a Universal leg machine.
I’m wondering if it is because I’m continuously going up hill (5-10% grade) to practice… or if my posture is wrong… or if my legs are just out of shape. I am consciously trying to put all of my weight on the seat as well. Any ideas/suggestions?
Thanks.
How long have you been riding? You may just need more time to build up those muscles and get in shape. When I started back up my quads killed me at first but after a few months I no longer have that issue, at least not to the same degree.
Other things to consider checking into:
Seat height - your knee should be slightly bent when your foot is at the bottom of your rotation. I think that has more to do with knee pain though.
When you’re a new rider you tend to tense up your legs and this tends to wear you out rather quickly. Even though you need to pedal harder uphill, still try and keep as much weight on the seat as possible.
Also like jbtilley said check your seat height, I find if I have it too low it burns out my quads much quicker.
Your legs just need to get used to riding, the more you ride, the better your technique will be, and your muscles will begin to grow accustomed to the new skills
Also, try riding slower and relax.
Thanks to all…
…the advice.
I made it a point today to be aware of when my leg muscles were tense… it was definitely ALL THE TIME 
I found myself sometimes not putting all my weight on the seat, not relaxing, and basically tensing up those quads. With concentrated effort to do the opposite of all those things it made things much better.
I think, too, that my legs are a bit out of shape.
I appreciate all the help. I increased my distance today… about 250’. Went up my driveway and around the cul-de-sac. 
By the way, I’ve always wondered what the ratio is of uni riders to non-riders. 1:50? 1:200? 1:500 It’s a select group…that is for sure.
You need to ride a whole lot before your legs are strong. Try riding as long and far as you can on flats, then when your legs are burned out, take a break, then do it again.
Some weeks of flat ground repeats will build up your legs for mild hill climbing, but to build up for the big stuff you’re gonna need to work harder and harder. It takes years to retrain your leg muscles for uni, unless of course you are already a biker like Lance 
It’s worth it, but leg pain ain’t half the work, wait till you head off road