I am not a fan of "weighted training". Rather strengthen your back muscles, work on core strength, and learn to properly use trekking poles. If you run you know about pace. Same concept for backpacking.

The difference in walking up a steep long hill w/o a pack and with a pack is more a matter of pace. A slow steady pace is best. Take a step forward, shift your body weight over the uphill foot, take a split-second rest, lift up your downhill foot and place above, repeat, repeat, repeat. Let your breathing determine the pace. Never get totally winded. A good guide should teach you proper pacing. Poor guides run up the hill to simply show their own abilities. Never feel compelled to go too fast. If the guide wants you to go faster, he can take some of your weight. That is what they are paid to do.

The Yosemite Falls trail is very rocky, has some big steps, and often the rock is covered with sand so you tend to slip. so if you may try practice hiking on a rougher surface than a sidewalk. I think going up is far better than going down this trail.

Can you get the pack they will give you before the trip? That way you can assure that the pack will be comfortable, and if not, have them give you a different pack. Having a well-fitting pack is highly important. Be sure they spend the time adjusting it properly. Most of the weight should be on your hips, not your shoulders. And how you pack it- weight distribution is also critical. They should help you with that too. If not, specifically ask for help.

If you are highly uncomfortable with a backpack, something is not right. It will be work, but should not be painful. Stop and adjust until you get it right.