For the sake of ease, lets say this backyard wedding is for 100 guests.
The following equipment is absolutely necessary for an outdoor affair:
tent including poles and sidewalls $2000
tent for caterer $150
13 60" round tables $107
2 8 ft banquet tables (head table) $16
5 cabaret tables (cocktails) $34
1 cake table $7
1 8 ft gift table $8
100 basic wood folding chairs $375
13 linens for dinner tables $468
2 linens for head table $59
5 cocktail table linens $105
1 cake table linen $23
1 gift table linen $29
100 napkins $60
dance floor $475
portable restrooms $1000
Total: $4916
Keep in mind that this is a ballpark figure and all the equipment (except for linens) is very basic. I also did not incorporate delivery and set up charges since they vary depending on the company and location but you can estimate at least $500 total.
Now that I have crunched the numbers for you go ahead and decide if an outdoor wedding is for you (and your budget!)