Any ideas on how to add more strength and/or lose weight on my monk?

[Kayso]

A lot of bad advice here, except from the Grandmaster.

I'm leveling a monk with my wife, a cleric, so I also look at STR as my major stat.

IFS > PB until late 40s in DPS. And when the PB does pass it, it's very close and it's time to work toward T-Staff or Epic and SoS instead.

First, I'll assume you know about STR soft caps and the fact the weight/AC issues on P99 seems to be less critical than on live. As such, I'll try to answer your questions as asked and look to increase STR and keep weight down. Avoiding any ridiculous expenditures, I'd suggest the following:

Ears: Farm Sarnak Earring of Station

Chest: Avoid the Living Fungus and Syythrak. Work toward RotLC. You'll need it anyway for epic. In the mean time, Crescent Gi from Dalnir is an upgrade, and I'll suggest you go there.

Neck: Would +5 AC and +5 FR be worth losing a point of Str? Runed Lava Pendant. Make a group and you can exp there.

Arms: Adamantite Armband, Lupine Rune get you more STR for less weight. Also, look at Crescent from Dalnir and Drake Hide -- no STR on either but they're light and have other nice stats.

Wrists: Hard Clay ($$$) and Granite are both 1.0

Legs: Crescent from Dalnir, Sarnak Hide ($$$). Maybe consider Gatorscale? HP is nice.

Hands: Work toward epic, obviously. Block Cutter have +1 Str over what you have and can be farmed near home or bought for ~400.

Feet: All the good STR boots are either heavy, expensive, or raid except Crescent from Dalnir.

Shoulders: Same as feet. Meditative blanket is lighter and slightly better. If you're willing to gain a bit, Obolus Death ($$$) or the Kerra Isle quest shoulders are considerations. Bloody mantle is also choice if you have friends you can muster for a kill.